Diamond-based microelectromechanical systems (MEMS) enable direct coupling between the quantum states of nitrogen-vacancy (NV) centers and the phonon modes of a mechanical resonator. One example, diamond high-overtone bulk acoustic resonators (HBARs), feature an integrated piezoelectric transducer and support high-quality factor resonance modes into the GHz frequency range. The acoustic modes allow mechanical manipulation of deeply embedded NV centers with long spin and orbital coherence times. Unfortunately, the spin-phonon coupling rate is limited by the large resonator size, >100 μm, and thus strongly-coupled NV electron-phonon interactions remain out of reach in current diamond BAR devices. Here, we report the design and fabrication of a semi-confocal HBAR (SCHBAR) device on diamond (silicon carbide) with f·Q>10 (10). The semi-confocal geometry confines the phonon mode laterally below 10 μm. This drastic reduction in modal volume enhances defect center coupling to a mechanical mode by 1000 times compared to prior HBAR devices. For the native NV centers inside the diamond device, we demonstrate mechanically driven spin transitions and show a high strain-driving efficiency with a Rabi frequency of (2π)2.19(14) MHz/V, which is comparable to a typical microwave antenna at the same microwave power, making SCHBAR a power-efficient device useful for fast spin control, dressed state coherence protection and quantum circuit integration.