The spin polarizabilities of the nucleon describe how the spin of the nucleon responds to an incident polarized photon. The most model-independent way to measure the nucleon spin polarizabilities is through polarized Compton scattering. Double-polarized Compton scattering asymmetries on the proton were measured in the $Delta(1232)$ region using circularly polarized incident photons and a transversely polarized proton target at the Mainz Microtron. Fits to asymmetry data were performed using a dispersion model calculation and a baryon chiral perturbation theory calculation, and a separation of all four proton spin polarizabilities in the multipole basis was achieved. The analysis based on a dispersion model calculation yields $gamma_{E1E1} = -3.5 pm 1.2$, $gamma_{M1M1}= 3.16 pm 0.85$, $gamma_{E1M2} = -0.7 pm 1.2$, and $gamma_{M1E2} = 1.99 pm 0.29$, in units of $10^{-4}$ fm$^4$.