The massive galaxy cluster El Gordo (z = 0.87) imprints multitudes of gravitationally lensed arcs onto James Webb Space Telescope Near-Infrared Camera (NIRCam) images. Eight bands of NIRCam imaging were obtained in the "Prime Extragalactic Areas for Reionization and Lensing Science" ("PEARLS") program. Point-spread function–matched photometry across Hubble Space Telescope and NIRCam filters supplies new photometric redshifts. A new light-traces-mass lens model based on 56 image multiplicities identifies the two mass peaks and yields a mass estimate within 500 kpc of (7.0 ± 0.30) × 1014M⊙. A search for substructure in the 140 cluster members with spectroscopic redshifts confirms the two main mass components. The southeastern mass peak that contains the brightest cluster galaxy is more tightly bound than the northwestern one. The virial mass within 1.7 Mpc is (5.1 ± 0.60)×1014M⊙, lower than the lensing mass. A significant transverse velocity component could mean the virial mass is underestimated. We contribute one new member to the previously known z = 4.32 galaxy group. Intrinsic (delensed) positions of the five secure group members span a physical extent of ∼60 kpc. 13 additional candidates selected by spectroscopic/photometric constraints are small and faint, with a mean intrinsic luminosity ∼2.2 mag fainter than L*. NIRCam imaging admits a fairly wide range of brightnesses and morphologies for the group members, suggesting a more diverse galaxy population in this galaxy overdensity.