One of the main challenges in spin qubits' studies associated with nitrogen vacancy impurities in diamond is to increase the coupling strength between the spins. With this task in mind we suggest a new type of a hybrid magneto-nano-electromechanical resonator, the functionality of which is based on a magnetic-field induced deflection of an appropriate cantilever that oscillates between nitrogen vacancy (NV) spins in diamond. Specifically, we consider a Si(100) cantilever coated with a thinmagnetic Ni film. As a new aspect of this study we utilize magnetoelastic stress and magnetic-field-induced torque to induce a controlled cantilever deflection. It is shown that, depending on the value of the system parameters, the induced asymmetry of the cantilever deflection substantially modifies the characteristics of the system. In particular, the coupling strength between the NV spins and the degree of entanglement can be controlled through magnetoelastic stress and magnetic-field-induced torque effects. Our theoretical proposal can be implemented experimentally with the potential of increasing several times the coupling strength between the NV spins. It finds that the coupling strength achieved by using our proposal enhances several times the maximal coupling strength reported before by Rabl et al. [P. Rabl, P. Cappellaro, M. V. Gurudev Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, Phys. Rev. B 79, 041302(R) (2009)].