  The magnetic interactions in the antiferromagnetic (AFM) Dirac semimetal
candidate SrMnSb$_2$ are investigated using \textit{ab initio} linear response
theory and inelastic neutron scattering (INS). Our calculations reveal that the
first two nearest in-plane couplings ($J_1$ and $J_2$) are both AFM in nature,
indicating a significant degree of spin frustration, which aligns with
experimental observations. The orbital resolution of exchange interactions
shows that $J_1$ and $J_2$ are dominated by direct and superexchange,
respectively. In a broader context, a rigid-band model suggests that electron
doping fills the minority spin channel and results in a decrease in the AFM
coupling strength for both $J_1$ and $J_2$. To better compare with INS
measurements, we calculate the spin wave spectra within a linear spin wave
theory, utilizing the computed exchange parameters. Although the calculated
spin wave spectra somewhat overestimate the magnon bandwidth, they exhibit
overall good agreement with measurements from INS experiments.
