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 the 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 bƃ, μ⁺μ⁻ and τ⁺τ⁻ channels are 90, 90 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. Copyright © 2016 American Physical Society.