do (one's) stuff
To do something that one is known to be skilled at. Maria is usually nervous before getting on stage, but once she goes out there and does her stuff, she's great—everyone always loves her presentations. OK, I'll get out of the way so you can do your stuff in the kitchen.
do stuff
To do non-specific tasks or activities. In this usage, a person is not stated between "do" and "stuff." Sorry I missed your call, I was doing stuff in the basement.