  Pressure-temperature phase diagram of the organic Mott insulator
$\kappa$-(ET)$_2$Cu$_2$(CN)$_3$, a model system of the spin liquid on
triangular lattice, has been investigated by $^1$H NMR and resistivity
measurements. The spin-liquid phase is persistent before the Mott transition to
the metal or superconducting phase under pressure. At the Mott transition, the
spin fluctuations are rapidly suppressed and the Fermi-liquid features are
observed in the temperature dependence of the spin-lattice relaxation rate and
resistivity. The characteristic curvature of Mott boundary in the phase diagram
highlights a crucial effect of the spin frustration on the Mott transition.
