I am reading a preprint titled Combinatorial Group Theory In Homotopy Theory I by Fred Cohen (available at Cohen's web page)
Now I need to find all papers whose references contain this preprint. Is there any way to do so? (By the way, I have access to Mathscinet.)
You will never be able to find all the papers that makes reference to a paper. One obvious limitation is that the paper making a reference has to be, somehow, listed on a webpage. It might not be the case (consider old manuscripts, technical reports that were never put on-line, etc.)
However, you can get satisfactory results by asking google sholar or Microsoft Academic Search, finding the reference, and click on "Quotes : x" or "Citations : y".
As the paper you are considering (Combinatorial Group Theory In Homotopy Theory I) was never published, things are getting worse: without any precise reference (as the journal, the conference, the year, and so on), it is hard to automatically list the papers making references to it.
The author is known both from google scholar and microsoft academic reasearch but it looks like none of them refer to the pre-publication you are considering.
Bonus : have a look at The work of Fred Cohen, section 8.