We discuss the problem of two-superparticle scattering in the framework of (2 + 1)-dimensional gauge theory of N = 2 Poincaré supergravity coupled to point sources. Our approach is the extension of our previous work for the case of (2 + 1)-dimensional Chern-Simons gravity, in which one of the particle is treated as a test particle scattering in the gravitational field of the other. We show that to relate the classical phase space of the particles to their space-time coordinates and momenta, it is necessary to take the gauge group to be the universal covering group of the N = 2 Poincaré supergroup. We also show that in the test particle approach, one of the superparticles is effectively a spinless particle. We explicitly calculate the corresponding scattering amplitude.