The superposition of frequency-shifted Laguerre-Gauss modes can produce a rotating saddle-like intensity profile. When spinning fast enough, the optical forces produced by this structured light saddle generate a dynamically stable equilibrium point capable of trapping nanoparticles in a high vacuum, akin to a Paul trap but with its unique characteristics. We analyze the stability conditions and center-of-mass motion, dynamics and cooling of a nanoparticle levitated in the optical saddle trap. We expect the optical saddle to find applications in levitated optomechanics experiments requiring fast parametric modulation and inverted squeezing potential landscapes.