A universal, torque-mixing method for magnetic resonance spectroscopy is presented. In analogy to resonance detection by magnetic induction, the transverse component of a precessing dipole moment can be measured in sensitive broadband spectroscopy, here using a resonant mechanical torque sensor. Unlike induction, the torque amplitude allows equilibrium magnetic properties to be monitored simultaneously with the spin dynamics. Comprehensive electron spin resonance spectra of a single-crystal, mesoscopic yttrium iron garnet disk at room temperature reveal assisted switching between magnetization states and mode-dependent spin resonance interactions with nanoscale surface imperfections. The rich detail allows analysis of even complex three-dimensional spin textures. The flexibility of microelectromechanical and optomechanical devices combined with broad generality and capabilities of torque-mixing magnetic resonance spectroscopy offers great opportunities for development of integrated devices.