I hope he doesn’t think I’m off prostituting myself.
I looked up "be off", seemed no right meaning.
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To be off doing something= Usually, you might be at a place such as home or work, if you are not there, you can be said to be off [doing something] by another person. It means not present at work, at home or at some other place where you are supposed to be or where you usually are.
It is constructed using: off + verb + ing + object [sometimes]. The idiom includes the gerund after off.
It is a shortened form of: to go off and do something.
So, in your sentence, off prostituting myself means: away from the place the person is expected to be and engaged in prostitution. The verb form here is to prostitute oneself.
In your cited context, the (optional) preposition could be any of off, away, out (and doubtless several others). Most if not all of those optional prepositions have little or no effect on the meaning, apart from the general implication of the hypothetical prostitution happening "somewhere else" (not where "he" or the speaker is, or more metaphorically doing something which is far away from one's normal behaviour.
(transcribed from comment)