The Joker had his knife at the left corner of Gambol's mouth, aiming and pulling the thing side/downwards. There are two things the Joker could have done in order to kill him:
1) Slash his face all the way down (not the Glasgow Smile), pressing firmly and tearing through the cheek, jaw, and on to the neck, severing both the left jugular vein and common carotid artery. This would explain why the Joker kept the black bag sticked on himself in order to avoid soiling his suit.
2) He playfully toys with the idea of slashing Gambol's face, giving him scars like his and all, but then decides to quickly stab the man through the soft palate, providing an easier access deep within the skull and sectioning large arteries including branches of the inner carotid artery in the process.
The latter is a personal favorite.
Now, I dunno the exact length of the Joker's knife... I guess it only has a few centimeters in it (about 10), but given that the guy loves to use these weapons to 'savor every emotion' in killing someone, he might have an idea as to the exact location and best angle necessaries to penetrate and damage or section part of the brain stem as well.
In any case, blame the PG rating for never showing us what truly happened.
EDIT: since Gambol simply drops and splats on the floor (as it should happen when the central nervous system gets damaged or destroyed), no external bleeding visible anywhere, and we don't even hear him gurgle or cough any blood which could happen had the joker chosen option 1 (laryngotracheal laceration), it further adds to the 2nd option hypothesis.
This should explain things better:
BTW I'm a general physician.