I use audacity. It is definitely capable of making more than one cut, though it's not the most obvious piece of software out there.
Sometimes I'll copy sections that I want to "cut" onto a new track and mute the master track so I can hear how the cuts sound. Then once I'm finished, I either delete the master one or just export the track with the cuts. YMMV.
A professional musician friend who helped me cut music once used a piece of software called Live. It looked pretty sophisticated and had some neat features, but it is not free.