Gamma-ray bursts (GRBs) as the most energetic explosions in the modern universe have been studied for over half a century, but the physics of the particle acceleration and radiation responsible for their observed spectral behaviors are still not well understood. Based on the comprehensive analysis of the pulse properties in both bright GRB 160625B and GRB 160509A, for the first time, we identify evidence of particle acceleration by relativistic magnetic reconnection from the evolutionary behavior of the two spectral breaks E p and E cut. Meanwhile, the adiabatic cooling process of the emitting particles in the magnetic reconnection regions produces a relation between the spectral index and the flux. We also discuss the physics behind spectral energy correlations. Finally, we argue that the identification of an anticorrelation between E cut and L iso may open a new avenue for diagnostics of the physics of the particle acceleration and radiation in a variety of astrophysical sources.