This Letter presents a numerical study of the interaction dynamics for the solitary waves of a nonlinear Dirac field with scalar self-interaction by using a fourth order accurate Runge-Kutta discontinuous Galerkin (RKDG) method. Some new interaction phenomena are observed: (a) a new quasi-stable long-lived oscillating bound state from the binary collisions of a single-humped soliton and a two-humped soliton; (b) collapse in binary and ternary collisions; (c) strongly inelastic interaction in ternary collisions; and (d) bound states with a short or long lifetime from ternary collisions.