We report on a pressure- (P-)induced evolution of superconductivity and spin correlations in CeIrIn(5) via the (115)In nuclear-spin-lattice-relaxation rate measurements. We find that applying pressure suppresses dramatically the antiferromagnetic fluctuations that are strong at ambient pressure. At P = 2.1 GPa, T(c) increases to T(c) = 0.8 K, which is twice T(c) (P = 0 GPa), in the background of Fermi-liquid state. This is in sharp contrast to the previous case in which a negative, chemical pressure (replacing Ir with Rh) enhances magnetic interaction and increases T(c). Our results suggest that multiple mechanisms work to produce superconductivity in the same compound CeIrIn(5).