Because he didn't have the power to, actually. One of the smarter moves that Mussolini had made in his slow slide into totalitarianism was to remove the power of the monarchy over him. This effectively tied Victor Emmanuel III's hands on what he could do to Mussolini - and it's important to not forget that Mussolini and the Fascists were outright popular with the populace of Italy until WWII started to sour the Italian people's patience.
When the Partito Nazionale Fascista (PNF) marched on Rome at the end of August 1922, high ranking members of the party (up to and including Mussolini) feared that Victor Emmanuel would get personally involved and have the army crush their rebellion. Furutre Italian Prime Minister Pietro Badoglio, then a general in the army, had given the King personal assurances that they could rout the Blackshirts with ease. Instead, Mussolini was invited to form a government as the King had lost faith in the Facta regime, and so had what was a seeming majority of the populace. Victor Emmanuel was willing to turn a blind eye to the distasteful actions of the PNF because of what they promised: an ordered Italy.
So Victor Emmanuel would turn a blind eye to many of the abuses of both Mussolini personally, and the PNF in general (to include openly assassinating political opponents, and a gradual removal of a democratic form of government). He further did nothing over a period of two years in which Mussolini essentially chopped his balls off and constitutionally tied his hands:
This move was possibly the smartest thing Mussolini ever did. Two powers were then granted to the GCF: they alone would have the power to not just choose the Party Secretary/Prime Minister (previously only the King could do this). Secondly, the GCF now controlled the monarchy's line of succession. The rub to all this? Every member of the GCF served at Mussolini's pleasure. Mussolini was now a dictator who on paper was subservient to the King, but effectively had rendered him powerless.
All this being said, history is ripe with dictatorships that are deposed when the people have had enough. Until Mussolini proved himself unpopular though, the King had very little legal recourse in which to unseat him. It wouldn't be until the Abyssinia campaigns that the storm to unseat Mussolini started to brew. Italian entry into Abyssinia was initially popular. Italians, fed by Fascist propaganda, were enthusiastically patriotic and in fact openly assaulted Prince Filippo Andrea Doria's (a staunch anti-Fascist) wife for refusing to contribute her wedding rings to the war cause. The King meanwhile was more than happy to enjoy the spoils of war. Afterall, Mussolini had gained him the crowns of Ethiopia and Albania in the process. To Victor Emmanuel, a vain man in private and an egotistical man in public, the successes of the Fascists served to illustrate that he made the correct decision in allowing Mussolini to power.
The first screw up of Mussolini was in the creation of the military rank of primo maresciallo dell'impero (First Marshall of the Empire). The rank was bestowed unto both Mussolini and Victor Emmanuel III, placing them nominally on equal footing as head of the military. Until this point the military belonged to the King and the King alone. Now for the first time in Italian history the royal family shared power with a Prime Minister. The King was not amused. He saw this as a direct assault on his power, and the first overt signs that Mussolini had designs on getting rid of him. This is when the first plans of intrigue from the palace began to swirl about Mussolini's fate. Still, Mussolini and the PNF were still popular - especially in the military which would be vital in deposing him. With the constitution amended to the point where the King more or less answered to Mussolini, there wasn't much he could do except express his displeasure.
What would ultimately doom Mussolini would be the missteps in Albania (which the King had oppossed), the disaster that was WWII, and the allies bombing Rome. Victor Emmanuel had reached his limit, but more importantly the Gran Consiglio del Fascismo had as well. What happened next saw a series of multiple designs at toppling Mussolini take effect. Both Dino Grandi and Marshal Pietro Badoglio were plotting with (and sometimes without) the King and the military itself had given Mussolini a strict deadline to end the war for Italy and remove itself from Germany's grasp. These plans were all accelerated by the bombing of Rome while Mussolini was in a meeting with Hitler at Feltre on June 19, 1943. A meeting of the Gran Consiglio on the night of July 24-25 saw all plans fall into place: Grandi (who had brought a live grenade with him in the event it was needed) proposed to the council that it recommend to Mussolini that the King resume control as commander of the Armed Forces. With Grandi highlighting that the choice of the council was to prove loyalty to either Mussolini or Italy herself, the council voted in favor of the measure. They also tasked Mussolini with delivering what was in effect a vote of no confidence to the King himself.
This vote of no confidence gave the plotters, and most importantly the King, all the impetus needed to complete their coup. That morning the King met with Badoglio to inform him that he would become the next Prime Minister, and that evening when Mussolini met with Victor Emmanuelle III to present the vote of no confidence the King informed him that it was time to step down. Mussolini is said to have agreed, as his spirits were quite broken at this time. What he was not expecting was that a platoon of Carabinieri were waiting outside to arrest him.
Ultimately to many, yes, Victor Emmanuel and the monarchy were doomed for siding with Mussolini and blamed in part for his actions. The status of the former royal family is a highly thorny subject in Italy. The referendum to abolish the monarchy only passed 12,717,923 to 10,719,284 votes. The initial Italian republican constitution held that all male members of the Savoy line were to be permanently exiled (with a male heir only entering the country in 2002 for an audience with the Holy See), while the constitution still holds that a republican form of government can not be replaced.