Cavity-enhanced radiation-pressure coupling of optical and mechanical degrees of freedom gives rise to a range of optomechanical phenomena, in particular providing a route to the quantum regime of mesoscopic mechanical oscillators. A prime challenge in cavity optomechanics has been to realize systems that simultaneously maximize optical finesse and mechanical quality. Here we demonstrate, for the first time, independent control over both mechanical and optical degrees of freedom within the same on-chip resonator. The first direct observation of mechanical normal mode coupling in a micromechanical system allows for a quantitative understanding of mechanical dissipation. Subsequent optimization of the resonator geometry enables intrinsic material loss limited mechanical Q-factors, rivalling the best values reported in the high megahertz frequency range, while simultaneously preserving the resonators' ultrahigh optical finesse. As well as providing a complete understanding of mechanical dissipation in microresonator-based optomechanical systems, our results provide a promising setting for cavity optomechanics.