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${\mathrm{SrMnSb}}_{2}$ is a candidate Dirac semimetal whose electrons near the $Y$ point have the linear dispersion and low mass of a Dirac cone. Here we demonstrate that ultrafast, 800-nm optical pulses can launch coherent phonon oscillations in ${\mathrm{Sr}}_{0.94}{\mathrm{Mn}}_{0.92}{\mathrm{Sb}}_{2}$, particularly an ${A}_{g}$ mode at 4.4 THz. Through first-principles calculations of the electronic and phononic structure of ${\mathrm{SrMnSb}}_{2}$, we show that high-amplitude oscillations of this mode would displace the atoms in a way that transiently opens and closes a gap at the node of the Dirac cone. The ability to control the nodal gap on a subpicosecond timescale could create opportunities for the design and manipulation of Dirac fermions.