I never understood this. Why does he kill them? Why can't he just mimic them and that's it?
Let's look at those that he copies.
The T-1000 stole his car and impersonates him for several days. If he'd left Austin alive, the car would have been reported stolen and his access to the Police computer revoked. There's a possibility that the car itself is lo-jacked and can be traced if reported stolen.
The aim here was to infiltrate the family and remain in situ in order to lure John to him. When that failed, the T-1000 killed Todd and left the bodies where they could be found. The more noise associated with John Connor, the greater the chance he'd get picked up by the police.
Security Guard Lewis
The goal here was to gain access to Sarah Connor. By killing the guard he can get into the Pescadero facility without fear that the staff would realise that there are twins walking around, potentially triggering an alarm.
One of the Terminator's secondary goals is the death of Sarah Connor, hence why it tried to kill her after it became apparent that she wouldn't give it assistance in hunting down her son.
So, what's with all the killing then?
The T-1000 is single-minded in its desire to fulfill its mission, killing John Connor. With that in mind, it kills anyone and anything that gets in its way, no matter how petty the advantage gained.
Because if he didn't, those persons could inadvertently inform his targets, just by showing in the wrong place or by phoning them while the T-1000 in mimic is trying to approach them.
The T-1000 (like the T-800 before him) is supposed to blend into the crowd. If there's a naked guy in the crowd pointing at him, yelling that he took his appearance, then his disguise has no value. Sure, he could lock them in a cellar, but given the "emergency" of his mission, it's more convenient to kill them on the spot and hide the corpse when needed. Corpses don't yell for help.
The terminators are built to kill humans. So, why wouldn't the T-1000 destroy them?
Also, it might blow its cover to have the real version of a person either walk into its infiltration or be found dead. It enhances the T-1000's chances of success to get rid of the person copied and destroy/hide the body.