This is a sub-page of A Hat in Time (Windows, Mac OS X)/Unused Animations.
There are actually two different Mafia models used in the game: Mafia_Greg and Mafia_Blender. Blender is older than Greg, and thus contains far more unused animations.
Mafia Greg
An extended animation for being scared if the player honks their scooter near one of them. This might've been intended for Goofy Mafia, during She Came From Outer Space.
An animation for stumbling while climbing a ladder. Mafia don't normally climb ladders in the final game, although Goofy Mafia uses animations for it in She Came From Outer Space.
An alternate animation for the Mafia around town that trip the player if they walk too close to them.
A leftover animation from the Prototype builds, this animation was used when holding Mustache Girl. It sees no use anywhere in the final game.
A version of Goofy Mafia's trembling animation, but without him holding a Time Piece.
An animation that appears to have been made for Mafia Boss's boss fight, but it isn't used. The animation used for the dashing Mafia in the boss fight have an intro part where they jump onto the stage and then charge. This animation is only the charge windup, and it's way slower than the one used in-game.
Mafia Blender
Kittens
Animations related to the scrapped box of kittens, which can be found in the Modding Tools. According to the filenames, these would've been used in some cutscene in Mafia Town, showing the Mafia holding an (unused) umbrella over the kittens, protecting them from the rain. The player would've then been given the option to take the kittens to their spaceship, according to Habboi.
What do you do when Mafia has kittens?
Maybe the Mafia aren't so bad after all.
This would've been so touching.
You wouldn't turn down a chance to adopt some adorable little kittens and save them from the rain, would you? Would you?
Misc.
A bunch of other animations for various things.
An animation for a Mafia shivering. Unknown purpose, but maybe the player would encounter Mafia in the freezer of Mafia HQ?
A Mafia looking miserable. A variant of this animation is used.
A Mafia starting to cry. Unknown what the context for this is.
An animation for chopping meat. There is a Mafia in the kitchen of Mafia HQ standing in front of some food, but he doesn't use this animation.
A Mafia fingering some poker chips in his hand. The poker chips model and its animation for this can be found in the Modding Tools.
A Mafia cheering, likely meant for the theatre in Mafia HQ during the Mafia Boss fight.