1. It slips off her arm.
2. It slipped off her arm.
Both #1 and #2 are fine in any kind of English.
3. It slips off of her arm.
4. It slipped off of her arm.
"Off of" on the other hand is a disputed usage. Some people dislike it, on the grounds that the "of" is superfluous; some people don't mind it, and believe that the "of" gives a greater sense of "off-ness" (i.e. that it intensifies the expression).
For my part, I don't mind it; but in contexts where your grammar may be subject to detailed scrutiny (e.g. in exams, interviews, job applications, etc.), it's probably better to avoid it.
All the best,
Student or Learner