The quantum spin liquid candidate NaYbSe$_2$ was recently reported to exhibit a Mott transition under pressure. Superconductivity was observed in the high-pressure metallic phase, raising the question concerning its relation with the low-pressure quantum spin liquid ground state. Here we combine the density functional theory and the dynamical mean-field theory to explore the underlying mechanism of the insulator-to-metal transition and superconductivity and establish an overall picture of its electronic phases under pressure. Our results suggest that NaYbSe$_2$ is a charge-transfer insulator at ambient pressure. Upon increasing pressure, however, the system first enters a semi-metallic state with incoherent Kondo scattering against coexisting localized Yb-$4f$ moments, and then turns into a heavy fermion metal. In between, there may exist a delocalization quantum critical point responsible for the observed non-Fermi liquid region with linear-in-$T$ resistivity. The insulator-to-metal transition is therefore a two-stage process. Superconductivity emerges in the heavy fermion phase with well-nested Yb-4$f$ Fermi surfaces, suggesting that spin fluctuations may play a role in the Cooper pairing. NaYbSe$_2$ might therefore be the 3rd Yb-based heavy-fermion superconductor with a very high $T_c$ than most heavy fermion superconductors.
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