Guillotine Guns are a new weapon type introduced during the Assassins Creed Unity: Dead Kings DLC.
"The Guillotine Gun is a powerful tool of destruction. It can be used in melee combat and as a devastating Ranged weapon."
These guns are a combination of a Mortar and an Axe. This allows them to fire off highly explosive rounds and inflict heavy damage in melee.
Firing a Mortar
Hold LB/L1 then RT/R2 to Aim. Release RT/R2 to fire. The attack has a wide blast radius so be sure you are either above the area or well back from it.