We introduce and investigate multivariate Tutte polynomials, dichromatic polynomials, subset-corank polynomials, size-corank polynomials, and rank generating polynomials of semimatroids, which generalize the corresponding polynomial invariants of graphs and matroids. We primarily establish their deletion-contraction recurrences, basis activities expansions, and various convolution identities. These findings naturally extend Kook-Reiner-Stanton's convolution formula and Kung's convolution-multiplication identities for the Tutte polynomials of graphs and matroids to semimatroids.