If it was just cut down.... you're first thing is to let it cure/dry.  Theoretically you can cut it into smaller sized pieces, but honestly it will still need a year or more of dry/cure time before it's ready to be stabilized (which I strongly recommend for this species of wood)   The wood needs to be 10% or less moisture content before it can be stabilized...otherwise it will warp and/or twist badly.   

Hunter,

Mesquite is a very hard, durable wood, that is somewhat difficult to work.  As Ed alluded, you will have to slice it, preferably into 1 inch thick boards, stack it, and wait a year or more in order for it to air dry.  Then check it with a moisture meter.  Once dry, it is exceptionally stable.  I will warn you that that the wood is often twisted, with splits, worm holes, and bark pockets (these are not suitable for knifemaking).  I have, however, seen some beautiful pieces made with mesquite.  If you wish to make use of the splits and/or worm holes, you may wish to experiment filling the gaps with black epoxy; it presents a beautiful contrast to the dark, rich color of the wood.

Sterling Sam, Instructor of Wood Technology & ABS Apprentice Smith