The three-dimensional Dirac semimetal $\mathrm{C}{\mathrm{d}}_{3}\mathrm{A}{\mathrm{s}}_{2}$ has attracted intensive attention recently for its exotic properties. Understanding the hot carrier excitation and its subsequent relaxation is a prerequisite for $\mathrm{C}{\mathrm{d}}_{3}\mathrm{A}{\mathrm{s}}_{2}$-based optoelectronics functional in the infrared (IR) and terahertz (THz) frequency range. In this work, the photoexcited hot carrier dynamics of a bulk single crystal $\mathrm{C}{\mathrm{d}}_{3}\mathrm{A}{\mathrm{s}}_{2}$ in the mid-IR has been explored by using the time-resolved pump-probe reflectance ($\mathrm{\ensuremath{\Delta}}R/R$) measurement at room temperature under a strong optical pumping. By combining the experimental $\mathrm{\ensuremath{\Delta}}R/R$ results and theoretical modeling, we analyzed the transient hot carrier redistribution upon a strong photoexcitation and the subsequent interband transitions. We show that the $\mathrm{\ensuremath{\Delta}}R/R$ response of $\mathrm{C}{\mathrm{d}}_{3}\mathrm{A}{\mathrm{s}}_{2}$ has a complex behavior, due to the interplay of transitions between Dirac bands and transitions involving both the Dirac and non-Dirac bands. Throughout the mid-IR region measured, we find that $\mathrm{\ensuremath{\Delta}}R/R$ is contributed primarily by changes in the refractive index, rather than by changes in the extinction coefficient. Our findings can help understanding the transient hot electron excitation and relaxation in $\mathrm{C}{\mathrm{d}}_{3}\mathrm{A}{\mathrm{s}}_{2}$ under an intense optical pumping, and provide a valuable reference for the $\mathrm{C}{\mathrm{d}}_{3}\mathrm{A}{\mathrm{s}}_{2}$-based ultrafast optoelectronics application.