As with many animations in games, Resident Evil 6 allows you to prematurely "cut" a reloading animation by quickly selecting a grenade type item (grenade, remote mine, first aid spray) and then switching back to your firearm.
As an alternative, you may also attempt to press the fire button (without aiming) to perform a gun-butt with the weapon, which also "completes" the magazine reload, but places your character in the gun butt animation. This, and other actions (taking cover, diving, etc.) may be faster or slower than weapon switching, but will depend on the situation you are in (esp. the very fluid situations in Mercenaries Mode).
This animation exploit allows you to cut down the animation cool-down periods for certain weapons (notably the grenade launcher), letting you fire the weapon a few moments earlier. This exploit does not apply to weapons with manually worked actions, such as the six-shot "Sniper Rifle", the regular shotgun, Piers' Anti-Material Rifle, etc.