Hi, I'm taking apart my bath tub I guess its fiberglass I'm cutting it in pieces because I don't know any other to do it, but I saw that it has a black drainage pipe right in the middle of the tub underneath. Is that connected some how and can I cut around it or do I have to disconnect it from the wall?

That "drainage pipe's ABS and it's my bet it connects to a trap that ties to the tub waste and overflow. Are you replacing the tub? If so, start by disconnecting the tub drain from the trap and do not cut the black drain pipe.
Good luck, Tom