It's possible - you can split audio tracks just like you can video. It's not so easy to split them in the right place though! Try setting markers as you preview the track and then split on them, or make sure you split shortly before and after the start and end points you want and then use a volume envelope to fade in / out.
Also remember that split points aren't hard edits into the file. You can easily move (trim) the end of the clip in or out after the fact to adjust the start and end points.