We investigate the evolution of spin polarization, spontaneous Hall angle (SHA), saturation magnetization and Curie temperature of $B2$-ordered Fe$_{60}$Al$_{40}$ thin films under varying antisite disorder, induced by Ne$^{+}$-ion irradiation. The spin polarization increases monotonically as a function of ion fluence. A relatively high polarization of 46 % and the SHA of 3.1 % are achieved on 40 nm thick films irradiated with 2 $cdot$ 10$^{16}$ ions/cm$^2$ at 30 keV. An interesting divergence in the trends of the magnetization and SHA is observed for low disorder concentrations. The high spin polarization and its broad tunability range make ion-irradiated Fe$_{60}$Al$_{40}$ a promising material for application in spin electronic devices.