As a part of the effort to investigate the implications of dark matter (DM)-nucleon effective interactions on the solar DM detection, in this paper we focus on the evaporation of the solar DM for a set of the DM-nucleon spin-independent (SI) effective operators. In order to put the evaluation of the evaporation rate on a more reliable ground, we calculate the non-thermal distribution of the solar DM using the Monte Carlo methods, rather than adopting the Maxwellian approximation. We then specify relevant signal parameter spaces for the solar DM detection for various SI effective operators. Based on the analysis, we determine the minimum DM masses for which the DM-nucleon coupling strengths can be probed from the solar neutrino observations. As an interesting application, our investigation also shows that evaporation effect can not be neglectd in a recent proposal aiming to solve the solar abundance problem by invoking the momentum-dependent asymmetric DM in the Sun.