The present work derived the robust constraints on annihilating WIMP parameters utilizing new radio observations of M31, as well as new studies of its DM distribution and other properties. The characteristics of emission due to DM annihilation were computed in the frame of 2D galactic model employing GALPROP code adapted specifically for M31. This enabled us to refine various inaccuracies of previous studies on the subject. DM constraints were obtained for all possible annihilation channels except $\chi\chi \rightarrow \gamma\gamma,\nu\bar{\nu}$. A wide variety of radio data was utilized in the frequency range $\approx$(0.1--10) GHz. As the result the thermal WIMP lighter than fiducially $\approx$(40--70) GeV was excluded in the case of light primary annihilation products $\chi\chi \rightarrow \tau^+\tau^-,\mu^+\mu^-,gg,c\overline{c},u\overline{u},d\overline{d},s\overline{s},e^+e^-,b\overline{b}$ (and an arbitrary combination of them). Heavier WIMP, which can annihilate to $W^+W^-,Z^0Z^0,t\overline{t},hh$; can not be probed at the level of thermal cross section, unless one assumes the optimistic cases of DM density and magnetic field distributions in M31. In summary, $m_x \gtrsim 40$ GeV represents the fiducial channel-independent mass limit for the thermal WIMP with the full uncertainty range estimated to be $\approx$(20--90) GeV. The obtained exclusions are competitive to those from Fermi-LAT observations of dwarfs and AMS-02 measurements of antiprotons. Our constraints significantly restrict the opportunity to explain the gamma-ray outer halo of M31 by annihilating DM. And, finally, we questioned the possibility claimed in other studies to robustly constrain heavy thermal WIMP with $m_x > 100$ GeV by radio data on M31.