What will happen to an airplane if you tilt one elevator up and the other down?

If you look up the Boeing F/A-18 Hornet, it does that exactly. It will create roll instead of standard pitch. On many fighter jets, this is common for when traveling at high speeds (exceeding Mach 1) or when drastic maneuvering is necessary. It works together with the ailerons to increase the roll rate of the aircraft.