What is the difference between 穿 and 穿上? I found the following sentence:


  我正在穿上毛衣。


In this sentence, can you rephrase it as the following?:


  我正在穿毛衣。


If you can rephrase it as such, is there any difference between 穿 and 穿上?

I also found the following sentence:


  他正在脱衣服。


Why don't you say it as possibly 脱下 but 脱? In other words, why do you have to use the particle when expressing putting on, but not when expressing putting off?
穿 and 穿上 are usually like English 'wear' and 'put on'.  The sentence 我正在穿上毛衣 means 'I am putting on a/the/my sweater'; I think this is quite unambiguous.  The sentence 我正在穿毛衣 is a little bit odd (to me), but can be interpreted as 'I am wearing a sweater'. 

穿上 is an action, which has a beginning, middle, and end. 穿 is often a state, if you like, with no beginning or end.  Not always of course: for example, in imperative sentences like 趕快穿衣服! "Hurry up and get dressed!" the 'hurry up' makes the non-stative meaning clear. You don't HAVE to use 穿上 to mean 'put on' then, but it helps make the action/state distinction explicit.  

脫 'to remove (clothing)' is unambiguously an action to begin with, so it doesn't need a resultative ending to disambiguate it.  脫下 is possible of course; to me it emphasizes both completion (clothes no longer on me) and a more detailed process. One example: I might use 脫 for removing shoes, 脫下 for a suit (jacket and pants).