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,
- For Teachers