Contact all the beat producers for ur mixtape and get their permission to use the beats. If the beat has a Sample from another work used in it, and the sample hasn't already been cleared, then u need to get permission from the original works owner.
Make a list of samples that are used in beats on the mixtape and contact
www.ascap.com, or
www.harryfox.com.
One of these orginisations should be able to answer your licensing questions.