The electronic reconstruction occurring at oxide interfaces may be the source of interesting device concepts for future oxide electronics. Among oxide devices, multiferroic tunnel junctions are being actively investigated as they offer the possibility to modulate the junction current by independently controlling the switching of the magnetization of the electrodes and of the ferroelectric polarization of the barrier. In this Letter, we show that the spin reconstruction at the interfaces of a ${\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}{\mathrm{MnO}}_{3}/{\mathrm{BaTiO}}_{3}/{\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}{\mathrm{MnO}}_{3}$ multiferroic tunnel junction is the origin of a spin filtering functionality that can be turned on and off by reversing the ferroelectric polarization. The ferroelectrically controlled interface spin filter enables a giant electrical modulation of the tunneling magnetoresistance between values of 10% and 1000%, which could inspire device concepts in oxides-based low dissipation spintronics.