The electric field control of functional properties is an important goal in oxide-based electronics. To endow devices with memory, ferroelectric gating is interesting, but usually weak compared to volatile electrolyte gating. Here, we report a very large ferroelectric field-effect in perovskite heterostructures combining the Mott insulator CaMnO3 and the ferroelectric BiFeO3 in its "supertetragonal" phase. Upon polarization reversal of the BiFeO3 gate, the CaMnO3 channel resistance shows a fourfold variation around room temperature, and a tenfold change at ~200 K. This is accompanied by a carrier density modulation exceeding one order of magnitude. We have analyzed the results for various CaMnO3 thicknesses and explain them by the electrostatic doping of the CaMnO3 layer and the presence of a fixed dipole at the CaMnO3/BiFeO3 interface. Our results suggest the relevance of ferroelectric gates to control orbital- or spin-ordered phases, ubiquitous in Mott systems, and pave the way toward efficient Mott-tronics devices.