The Blue Slime is an extra mob that was added from Tinkers Construct. When killed, it drops Gelatinous Slime, which you can eat as food, or use as an alternative to green slime. It can also be used to make Slime Brick, Slimy Mud, and Slime Crystals.
Blue Slimes have 3 different sizes; big, medium and small.
The big slime has 24 HP, and breaks up to the medium version when killed.
The medium slime has 12 HP, and breaks up to the small version when killed.
The small version has 4 HP, and is still aggressive, but seems to do no damage to a player.
NB: They can also carry other mobs, making them an even harder enemy to defeat, and they can break up into a rare (and ultra?) version of the mob, so be on your guard.