The negatively-charged silicon-vacancy (SiV\(^-\)) color center in diamond has recently emerged as a promising system for quantum photonics. Its symmetry-protected optical transitions enable creation of indistinguishable emitter arrays and deterministic coupling to nanophotonic devices. Despite this, the longest coherence time associated with its electronic spin achieved to date (\(\sim 250\) ns) has been limited by coupling to acoustic phonons. We demonstrate coherent control and suppression of phonon-induced dephasing of the SiV\(^-\) electronic spin coherence by five orders of magnitude by operating at temperatures below 500 mK. By aligning the magnetic field along the SiV\(^-\) symmetry axis, we demonstrate spin-conserving optical transitions and single-shot readout of the SiV\(^-\) spin with 89% fidelity. Coherent control of the SiV\(^-\) spin with microwave fields is used to demonstrate a spin coherence time \(T_2\) of 13 ms and a spin relaxation time \(T_1\) exceeding 1 s at 100 mK. These results establish the SiV\(^-\) as a promising solid-state candidate for the realization of scalable quantum networks.