The studying of how twisted light interacts with chiral matter on the nanoscale is paramount for tackling the challenging task of optomechanical separation of nanoparticle enantiomers, whose solution can revolutionize the entire pharmaceutical industry. Here we calculate optical forces and torques exerted on chiral nanoparticles by Laguerre-Gaussian beams carrying a topological charge. We show that regardless of the beam polarization, the nanoparticles are exposed to both chiral and achiral forces with nonzero reactive and dissipative components. Longitudinally polarized beams are found to produce chirality densities that can be 109 times higher than those of transversely polarized beams and that are comparable to the chirality densities of beams polarized circularly. Our results and analytical expressions prove useful in designing new strategies for mechanical separation of chiral nanoobjects with the help of highly focussed beams.