Snap-through mechanisms are pervasive in everyday life in biological systems, engineered devices, and consumer products. Snap-through transitions can be realized in responsive materials via stimuli-induced mechanical instability. Here, we demonstrate a rapid and powerful snap-through response in liquid crystalline elastomers (LCEs). While LCEs have been extensively examined as material actuators, their deformation rate is limited by the second-order character of their phase transition. In this work, we locally pattern the director orientation of LCEs and fabricate mechanical elements with through-thickness (functionally graded) modulus gradients to realize stimuli-induced responses as fast as 6 ms. The rapid acceleration and associated force output of the LCE elements cause the elements to leap to heights over 200 times the material thickness. The experimental examination in functionally graded LCE elements is complemented with computational evaluation of the underlying mechanics. The experimentally validated model is then exercised as a design tool to guide functional implementation, visualized as directional leaping.