Well... It wasn't so much Hitler as much as it was Hitler's commanders. In particular, it was Gerd von Rundstedt, commander of the German Army Group A, that made the decision. You see, at the start of WW2, Hitler did not micromanage his military as much, leaving quite a bit of the decisions to the discretion of his commanders.
To understand Dunkirk, we must go first to the opening stages of the Battle of France. When Germany invaded, the French had a long line of fortifications (the Maginot Line) facing the German border. The French expected that the Maginot Line would force the Germans to attack France through Belgium. This was exactly what happened, but Belgium can be roughly divided into two regions: the lowlands, and a heavily-forested stretch known as the Ardennes. The French knew that the Germans were good at tank warfare, and since the Ardennes was poor tank country, they thought the main attack would come through the lowlands. The Ardennes was also very rugged, and the French believed it would take the Germans at least a week to get through. Since the French expected that the majority of the German forces could be committed to the lowlands, that is where they sent their elite forces. Some forces were assigned to defend the Ardennes approach, but they were basically the weaker, poorer-trained parts of the French military.
So, what the Germans did, was that they took a big gamble and it paid off. They committed much of their best forces to the Ardennes approach while launching a simultaneous phoney attack at the lowland approach. This deceived the Allied forces (French, British, and Belgian) into believing they were in the right place, while the elite German forces swept aside the weaker part of the French as well as Belgian forces and broke through into France. Their motorized, armoured divisions leading the charge, the Germans had made it past the Ardennes in two days rather than a week. By 19 May, 1940, the Germans had destroyed the French forces (primarily the French Ninth Army) guarding the Meuse River that faced the Ardennes approach. The best of the French forces and their British allies, who had hitherto been preoccupied fighting off phoney attacks, were now cut off from the rest of France.
By May 21, the Allies realized they were basically surrounded by the enemy and stuck in Belgium. German forces were quickly moving to encircle the Allies. The French forces stuck in the north were ordered to fight their way south, to reunite with the rest of the French military. The British on the other hand, were not operating on entirely the same orders as the French, and poor communication between the Allies even led to friendly fire. The British did, however, participate in the planned French counterattack against the Germans to break out. This was called the Battle of Arras, and it was a failure. Although Allied forces made early gains, the Germans (particularly Rommel's division) quickly organized a defensive response. Bad communication between the Allies made them slow to take advantage of potential opportunities, and the Allies suffered heavily.
What the Battle of Arras did do, however, was put a scare into the German commanders. During the Battle of Arras, the Germans realized that the speed of their advance meant that some tank divisions had outrun the infantry divisions, leaving tanks without infantry support and vice versa. German commanders worried about being outflanked. Although Rommel successfully held his ground, he made alarmist claims that he had been attacked by hundreds of British tanks (when the reality was 88 tanks, more or less), and was in favor of sitting tight until the infantry divisions caught up. The Germans basically felt like they had overextended themselves, and despite beating back the Arras counterattack, they feared they might not be able to fend off a second counterattack (unaware of the dire straits of the Allies post-Arras). In light of these considerations, the leading commander of the German forces in the area, Gerd von Rundstedt, called for a halt in the German advance.
Rundstedt estimated the infantry needed 36 hours to catch up, when in reality it took 48 hours before the German advance could resume.
This brief period of respite allowed the British to rally themselves after the chaos at Arras, and they retreated to the English Channel, to the beaches of Dunkirk, where the evacuation of 400,000 British soldiers trapped there would begin.
After the Germans regrouped, they did exactly as you said, and tried to crush the British army stranded in Dunkirk while they had them cut off and surrounded. Only this wasn't as easy as it sounded. Remember, there was still a French component stuck on the wrong side of France with the British, and they fought valiantly in the face of near-certain defeat with desperate rearguard actions. Also, you must factor in the British Royal Air Force and the British Royal Navy's contributions. The RAF in particular flew over 3,500 sorties, using 16 squadrons, and met the Luftwaffe in fierce dogfights that exacted a heavy toll on the German bombers. Because the RAF's dogfights took place far from the beaches (if the Luftwaffe reached the beaches it was already too late, they had broken past the RAF), much of the Army was unaware of the RAF's brave attempts to protect them. Many soldiers thus bitterly complained about the RAF doing nothing to help, painfully unaware of the pilots fighting and dying in the skies far away from them until they had safely returned home. In essence, all this manage to delay the Germans long enough for the British to escape.
Keep in mind that while the German halt order after Arras may have bought valuable time for the British to evacuate from Dunkirk, the Germans were probably in need of a halt order anyway. Their armored divisions were way ahead of their supporting infantry, and they had been fighting all the way from the Ardennes; they were in dire need of repair and refueling.
TL;DR version, Hitler/the Germans did not crush the British army while he had it surrounded and cut off at Dunkirk, because in the sheer impetus of the blitzkrieg into France, his infantry hadn't caught up to his tanks/armour, and the tanks/armour needed rest, repair, and refueling. The Germans then got hit with a counterattack by Allied forces trying to break out of the German encirclement, got scared, and decided to halt and catch their breath. Once they were regrouped and recovered, the Germans did their best to crush the British at Dunkirk, but ultimately failed due to the valiant yet doomed French forces fighting a rearguard action and the bravery of both the British Navy and the Air Force coming to the rescue of the trapped Army.
Hope this helped!
Sources:
Horne, A. (2007). To Lose a Battle: France 1940. Penguin UK.
Bond, Brian (1990). Britain, France and Belgium 1939–1940 (2nd ed.). London: Brassey's. ISBN 0-08-037700-9.
Atkin, Ronald (1990). Pillar of Fire: Dunkirk 1940. London: Sidgwick & Jackson. ISBN 0-283-99697-8.
Cooper, M. (1978). The German Army 1933–1945, its Political and Military Failure. Briarcliff Manor, NY: Stein and Day. ISBN 0-8128-2468-7.
Marix Evans, Martin (2000). The Fall of France: Act with Daring. Oxford: Osprey. ISBN 1-85532-969-7.
Blaxland, Gregory (1973). Destination Dunkirk: The story of Gort's Army. London: William Kimber. ISBN 978-0-7183-0203-0.
EDIT: Whoa, my first gold post! Super honored, even more so because it was from /r/askhistorians. Cheers!
EDIT 2: Oh, wow, a double gold post! Not sure what to say! Thanks heaps!
Others have commented on the situation from the perspective of the German ground forces. I'd add that Herman Goring, who was in charge of the Luftwaffe, prevailed on Hitler to allow the Luftwaffe to 'finish off' the British army by themselves. At the time, Goring was part of Hitler's inner circle, and so he did have some influence over the dictator. Goring argued that A) the Luftwaffe was capable of the job, and B) that if the victory over the British was attributed to the Luftwaffe, it would be better politically for Hitler. Unlike the Wehrmacht, the Luftwaffe was seen as having strong links with the Nazi party. This is because an air force was forbidden by the Treaty of Versaille, and the Luftwaffe was only established once Hitler openly renounced the treaty (although Germany had been developing an air force in secret for some years beforehand). A victory for the Luftwaffe thus reflected well on the Nazis, moreso than a Wehrmacht victory.
On Goring's part, he was likely jockeying for position within Hitler's inner circle (as other leading Nazis did). He wanted to impress Hitler and prove his own capabilities. Unfortunately for the Nazis, from what we know of the Luftwaffe, Goring did not take much genuine interest in understanding air warfare and perhaps overestimated the Luftwaffe's capabilities. Hitler likewise did not understand air warfare. Additionally, the weather (and the RAF) frustrated the Luftwaffe's efforts, and Goring probably did not want to admit his failure even once this became clear.