We report that complete spin polarization and controllable spin polarization of carriers can be simultaneously realized in the Heusler alloy Mn₂CoAl simply by applying external pressures based on first-principles studies. At ambient conditions, Mn₂CoAl is a ferromagnetic spin-gapless semiconductor (SGS) with complete spin polarization. Under hydrostatic pressures up to 40 GPa, Mn₂CoAl undergoes a series of electronic transitions from SGS with spin-up as a conducting channel to a ferromagnetic semiconductor and then to SGS with spin-down as a conducting channel and finally to a half metal, during which the magnetic moment remains as 2 μ_B. Such rich electronic transitions are attributed to different responses of the spin-up and spin-down electrons under pressure. This work highlights a desirable way to control the carrier's spin polarization and provides a new insight into the electron behavior in Mn₂CoAl related Heusler alloys under pressure.