I have a CIFS share mounted on a Linux machine. The CIFS server is down, or the internet connection is down, and anything that touches the CIFS mount now takes several minutes
There's a -f option to umount that you can try:
umount -f /mnt/fileshare
Are you specifying the '-t cifs' option to mount? Also make sure you're not specifying the 'hard' option to mount.
You may also want to consider fusesmb, since the filesystem will be running in userspace you can kill it just like any other process.