At present the world's largest sample of 1.3 billion J/psi decay has been collected by the BESIII detector, which provides a unique opportunity to investigate light meson decays. The $a^0(980)-f^0(980)$ mixing is an important probe to the nature of those two light scalars. The first observation of $a^0(980)-f^0(980)$ mixing will be reported. The $\eta$ and $\eta'$ hadronic decays are sensitive tools for the investigations of $\pi-\pi$ and $\eta-\pi$ interactions, symmetry breaking, and for testing the Chiral Perturbation Theory. In this talk, BESIII presents new results on amplitude analyses of the Dalitz decays $\eta'\to 3 \pi; \eta' \to \eta \pi \pi, \eta'\to \gamma \pi \pi$, on the observation of new decay modes and on searches for rare or forbidden decays.