We present optically tunable magnetic three-dimensional (3D) metamaterials at terahertz (THz) frequencies which exhibit a tuning range of ~30% of the resonance frequency. This is accomplished by fabricating 3D array structures consisting of double-split-ring resonators (DSRRs) on silicon on sapphire, fabricated using multilayer electroplating. Photoexcitation of free carriers in the silicon within the capacitive region of the DSRR results in a redshift of the resonant frequency from 1.74 to 1.16 THz. The observed frequency shift leads to a transition from a magnetic-to-bianisotropic response as verified through electromagnetic simulations and parameter retrieval. Our approach extends dynamic metamaterial tuning to magnetic control, and may find applications in switching and modulation, polarization control, or tunable perfect absorbers.