He pulled the cap off of the marker.
He pulled the cap off the marker.
He pulled off the cap/He pulled the cap off.
The first two sentences convey the same meaning; there's no difference. The phrasal/compound preposition "off of" instead of the preposition off without of, though disapproved by some people, is commonly used in informal American English. So there's nothing wrong with the phrasal preposition off of.
As for the third sentence, the "off" has been used as an adverb to say that the cap was removed by pulling it from something. you don't use this word as an adverb with "of". The said sentence is also grammatical. Some more examples are:
He shaved his beard off
Take your coat off.
So the difference between the first two sentences and the third sentence in question is that in the former case off and off of are prepositions whereas in the latter case off is an adverb. The former shows that the cap was removed by pulling it from the marker and the latter means that the cap was removed by pulling it from something not mentioned.