Mechanical strain tuning of magnetic properties is crucial for developing flexible electronic and spintronic devices. Here, (111)-oriented CuFe2O4 (CuFO) thin films are epitaxially grown on flexible mica substrates, and the influence of the mechanical strain on magnetic properties is investigated by altering the curvature of the CuFO/mica structures. Both the in-plane and out-of-plane saturation magnetic moments increase monotonously with the decrease of bending radius, which can be ascribed to the mechanical strain-induced Jahn-Teller distortion and much easier neighboring ferromagnetic domain switching in the CuFO films. Particularly, the residual magnetization can be dramatically enhanced by mechanical strain with a large gauge factor of 321.25, demonstrating effective strain tuning of magnetism. Moreover, the CuFO/mica structures exhibit strain tunable parallel magnetic anisotropy and excellent mechanical antifatigue properties. This work implies a great potential for promissing applications in flexible spintronics and electronics.