So I have these earphones to listen to music with. One of them don't work, so if I cut off that earphone will it effect the other?
Why didn't you just buy a new set? I can get earbuds for less than $5, but I get the Apple ones for my iPod because I like the convenience of the remote.
I do not think that it will be a good idea to cut off the fault piece. The two have a connection and getting rid of one might affect the performance of the working piece. You may consider repairing the fault one, instead of getting rid of it.