  Dirac matters provide a platform for exploring the interplay of their
carriers with other quantum phenomena. Sr$_{1-x}$Mn$_{1-y}$Sb$_2$ has been
proposed to be a magnetic Weyl semimetal and provides an excellent platform to
study the coupling between Weyl fermions and magnons. Here, we report
comprehensive inelastic neutron scattering (INS) measurements on single
crystals of Sr$_{1-x}$Mn$_{1-y}$Sb$_2$, which have been well characterized by
magnetization and magnetotransport measurements, both of which demonstrate that
the material is a topologically nontrivial semimetal. The INS spectra clearly
show a spin gap of $\sim6$ meV. The dispersion in the magnetic Mn layer extends
up to about 76 meV, while that between the layers has a narrow band width of 6
meV. We find that the linear spin-wave theory using a Heisenberg spin
Hamiltonian can reproduce the experimental spectra with the following
parameters: a nearest-neighbor ($SJ_1\sim28.0$ meV) and next-nearest-neighbor
in-plane exchange interaction ($SJ_2\sim9.3$ meV) , interlayer exchange
coupling ($SJ_c\sim-0.1$ meV), and spin anisotropy constant ($SD\sim-0.07$
meV). Despite the coexistence of Weyl fermions and magnons, we find no clear
evidence that the magnetic dynamics are influenced by the Weyl fermions in
Sr$_{1-x}$Mn$_{1-y}$Sb$_2$, possibly because that the Weyl fermions and magnons
reside in the Sb and Mn layers separately, and the interlayer coupling is weak
due to the quasi-two-dimensional nature of the material, as also evident from
the small $SJ_c$ of -0.1 meV.
