No, don't do that. The 4 pin connector provides the power while the 3 pin connector only allows you to monitor the RPMS via the motherboard monitor. If you cut the red and black wires, then your fan will not be powered. Your best bet is to cut the black and red wire, crimp them with the small pins and place them in the 3 pin connector. Make sure you use a diagram that shows you the wire configuration, if you transpose the red and black wires, it could get ugly.
Edit: Changed minor details and typos.