On the Machiniste, click the EXCL. buttons next to each sample you want to choke. Highest sample has playback priority. The TR808 unfortunately doesn't have a choke feature. Your best bet is to tweak the decay of the choked sound so that it doesn't run past the start of the other one.
As an alternative on the 808 and 909 devices, you can use the note track to place a note with a velocity of 1 where you want to cut the previous note. A note with a velocity of 0 does not register on these devices but does register on the Machiniste.
hold more than one 808 by the throat at the same time.