  Recent gamma-ray observations and radio observations put strong constraints
on the parameters of dark matter annihilation. In this article, we derive new
constraints for six standard model annihilation channels by using the recent
radio data of M31 galaxy. The new constraints are generally tighter than the
constraints obtained from 6 years of Fermi Large Area Telescope gamma-ray
observations of the Milky Way dwarf spheroidal satellite galaxies. The
conservative lower limits of dark matter mass annihilating via $b\bar{b}$,
$\mu^+\mu^-$ and $\tau^+\tau^-$ channels are 90 GeV, 90 GeV and 80 GeV
respectively with the canonical thermal relic cross section and the Burkert
profile being the dark matter density profile. Hence, our results do not favor
the most popular models of the dark matter interpretation of the Milky Way GeV
gamma-ray excess.
