(Can I take thi-satof?)
Yes - if you're drunk and slurring your speech.
The correct expression would be:
May I take my hat off?
"Do you mind if I take my hat off."
But in your example, the words are pronounced separately, not slurred together; though in moving the mouth around quickly enough to follow the 'a' sound in 'hat' with the 'o' sound in 'off', it might seem as if 'hatoff' is being said.
Student or Learner