How can I power a three phase AC motor with only 2 phases?
Three phase motors need to be fed with three phase power. It has to do with the internal configuration, each power leg must be fed power 120 degrees apart so the created magnetic field spins the rotor.

If you're thinking about using 240V split phase to power this motor, the effecive phase angle between each leg and neutral is 180 degrees out of phase. Expect the motor to stall if it will even begin to spin weakly, not create the proper back EMF, draw high current and release smoke.

If you need to run this motor off of split phase, you need to run it from 240V single phase and use a phase converter that electrically produces three phase power output. Your motor will then run perfectly. There are two types of phase converter, Motor Generator and Static (electronic).

Differences between Split Phase 240VAC and 3-phase 240VAC