#1, Don't slip the clutch, let off the gas! The clutch is not for traction control. I have no idea why you would slip the clutch in reaction to not hooking up. That is a horrible idea.
#2, Limited slip diff
#3, Sticky tires
There's no magic want for this. 350+whp is a lot to put down through two 245-275mm street tires in 1st gear. Don't peg the throttle so hard in 1st. Leave TC on until you know how to drive the car.
2009 BMW 135i, 6 MT, M Sport, DIY DCI, Cobb AP, Apex 18x8.5+9.5, 235/265 Starspecs