How to make an Ableton Live project a set time
Go into arrange view, expand the master track

Enter draw mode: press ctrl+b or click on the pencil button at the top of the screen next to the little keyboard. You want it to be yellow.

Use draw mode to zero out a region of the Master Mixer - Track Volume automation

Exit draw mode: press ctrl+b again, or click on the pencil button so that it is no longer active.
Use the pointer cursor to click on one of the automation corners to the right, deleting it.

Delete the other rightmost automation corner. Now the automation curve should be down at the bottom for the rest of time.