I'm seriously considering to change the behavior so that mouse triggering (using the play button) is monophonic (when you trigger one arragnement the playing arrangement is stopped) and then perhaps add a feature to right click an arrangement and have it play on top of the others (and it won't be stopped when another arrangement is triggered) - this would be the best solution I think, albeit a bit complex perhaps...
Note that what GilJ identified is the "trigger with host" feature that plays the selected arrangement as soon as the host sequencer starts, and forces monophonic arrangement playback changing arrangements via midi or mouse.
In any case I recommend you get used to triggering LiveSlice via midi, because it can be recorded - your mouseclicks can't.
Now if that wasn't confusing I dunno what confusing is

