Magnetic nanoparticles (MNPs) constitute promising nanomedicine tools based on the possibility of obtaining different actuations (for example, heating or mechanical response) triggered by safe remote stimuli. Particularly, the possibility of performing different tasks using the same entity constitutes a main research target towards optimizing the treatment. But such a goal represents, in general, a very difficult step because the requisites for achieving efficient responses for separate actuations are often disparate - if not completely incompatible. An example of this is the response of MNPs to external AC fields, which could in principle be exploited for either magneto-mechanical actuation (MMA) at low frequencies (tens of Hz); or heat release at high frequency (0.1-1 MHz range) for magnetic fluid hyperthermia (MFH). The problem is that efficient MMA involves large torque, the required material parameters for which are detrimental to high heating, thus hindering the possibility of effective alternation between both responses. To overcome such apparent incompatibility, we propose a simple approach based on the use of anisotropic MNPs. The key idea is that the AC-frequency change must be concurrent with a field-amplitude variation able to promote - or impede - the reversal over the shape-determined anisotropy energy barrier. This way it is possible to switch the particle response between an efficient (magnetically dissipationless) rotation regime at low-f, for MMA, and a "frozen" (non-rotatable) high-energy-dissipation regime at high-f, for MFH. Furthermore, we show that such an alternation can also be achieved within the same high-f MFH regime. We use combined Brownian dynamics and micromagnetic simulations, based on real experimental samples, to show how such a field threshold can be tuned to working conditions with hexagonal-disk shape anisotropy.