I meant to write a brief intro then link you to a good answer on the subject but I kind of rambled. I'll put the answer up front and leave my rambling at the bottom!
This question expresses some of the modern misconceptions of the Assyrian and u/udreaudsurarea explains them
From the middle of the 9th century BC, but particularly after 745, they were a very centralized, militaristic state. The kings, for example, would count the years of their reign not by years but by "campaigns." The king's achievements for the year would often be a list of defeated enemies.
It's unlikely the kings could mount meaningful campaigns literally every year, and some years may simply have been relatively peaceful but it gives you an idea of how people saw the king and their empire. And because of an apparently heavy handed system of taxation and tribute there were often rebellions to be quelled (I sometimes wonder if the kings felt like me struggling to fill out a weekly activity report at work). This mindset drives a lot of the documents that were produced during this time, which in turn drives much of the modern public perception.
Warfare everywhere in the ancient world was harsh, and conquered peoples, particularly rebels, were often subject to mass deportation. People didn't like being defeated and if left in place would plot rebellions and other types of resistance so simply relocating somewhere distant was a straightforward way to deal with this. In addition the resources provided by the people (specialized craftspeople for example) were legitimately valuable. This is usually seen as particularly cruel by modern observers but this was standard operating procedure for the ancient near east for a long time before. Assyria, by virtue of its size and frequent warfare, did this on a scale not seen before.
And while the deported people no doubt hated it, they were in many ways an important resource to the empire and there's evidence they were cared for on their journey (i.e. this was not intended to be a death march) and on arrival they were not slaves but part of the rest of the citizenry of the empire. I don't want to speak for the people but this doesn't seem like a fate worse than death and when terrible death is on the table that's a good deal (though psalm 137, for example, really drives home how much people hated this - mind you that psalm is actually about Babylon not Assyria, to my point this was a common tactic).
This massive relocation and intermingling of populations led to things like the Aramean language becoming the lingua franca, a role it would hold for many centuries.
You can compare the neo-Assyrians to their immediate successors, the neo-Babylonians. Babylonian kingship focused on things like building and their inscriptions focus on that instead of warfare. Well, the Babylonians still fought - the most famous mass deportation in history is the Babylonian deportation of the Jews after the violent and destructive sack of Jerusalem (hence Psalm 137). The Babylonians, new boss same as the old boss in that respect. The Babylonians didn't rule nearly as long though before becoming part of the fledgling Persian empire which had a completely different approach to statecraft (an approach we generally consider much "nicer").
Edit: one more thing I'd add about their reputation - they definitely, through propaganda and actions, cultivated an idea of "calculated frightfulness" (a term you see used in various places). Actually besieging and attacking a city was expensive, time consuming, and difficult (Sennacherib received biblical fame for failing to take Jerusalem, for example, though in his own inscriptions he speaks of successfully locking them up like a bird in a cage). They didn't really want to fight a protracted battle or siege, they wanted the enemy to surrender (which would usually ensure less harsh treatment). To help in that matter they were absolutely brutal on their way through enemy territory, approaching an enemy city. Essentially saying look at the terrible things we can do to people and land, this is your fate if you don't surrender. Again, no ancient state would shy away from this tactic if they thought it would work. The "nice" Persians I mentioned earlier seem to have used a similar tactic after they fought their one major battle against the Babylonians, at Opis. After winning, Cyrus the great (immortalized in the Hebrew bible as the good ruler who ended the Jewish exile) slaughtered the inhabitants after winning which immediately caused the nearby city of Sippar to capitulate without a fight, and Babylon seems to have followed suit as well.