You can set this up fairly easy.
First up i assume you're using user1 or user2 mode to stop tracks and assigning the midi to the stop button at the top of live.
Different approach would be to assign it to the "stop clips" button at the bottom of your 'scene launch' section (look up and down the master channel in session view)
This will stop all clips but keep the track going.
If you want to change the stop button so that it doesn't stop at the end of the bar, it stops instantly, the only way I know of is to change the global quantisation to "none". This will mean though, that your clips will also be able to launch out-of-sync. Perhaps a better method would be to turn the global quantisation to 1/8 or 1/16 (or if u got super fast fingers, 1/32) and then that way you can stop it CLOSE to instantly, but you also launch clips in sync (unless you're 1/32 too slow!)
Also you could go into mixer mode on the launchpad, then one of the 'scene launch' buttons down the side of the launchpad (the one with "stop" next to it) becomes a 'stop all clips' button (ie you don't need to assign it in user1 mode, it's there ready to use
Hope that helps!
Using Ableton for Composing/Remixing/DJing
Macbook 2.26GHz/8GB/500GB/7200rpm/OSX Lion
ZeRO SL MkII & Launchpad
Reloop 10tion - Behringer Truth 1030A's - Sennheiser HD280's
Ableton Suite 8.2.2 - Automap Pro 3.7
http://soundcloud.com/jbainesy