By mistake, unwanted references are present in my accepted manuscript and I want to remove them from my author proof copy. Will the manuscript go to the editor once again or not?
At the author proof stage, you are expected to not make any more substantive changes. Thus, if the copyeditors introduced these unwanted references, there is zero problem in asking for them to be removed.
If you realize that you messed up any put in things that you should not have or wish that you had not, however, it's a bit more iffy. You can ask to have them removed and the journal staff will make a judgement call of whether it requires reconsideration or not. If it's a simple mistake, don't worry about it. If you were to try to remove all references to prior work, on the other hand, they would be right to consider that a serious substantive change and to strenuously object.
Bottom line: just explain why you want the references removed, and if it's reasonable don't worry about it.