We use Lightcone Conformal Truncation to analyze the RG flow of the two-dimensional supersymmetric Gross-Neveu-Yukawa theory, i.e. the theory of a real scalar superfield with a DOUBLE-STRUCK CAPITAL Z(2)-symmetric cubic superpotential, aka the 2d Wess-Zumino model. The theory depends on a single dimensionless coupling (g) over bar, and is expected to have a critical point at a tuned value (g) over bar (*) where it flows in the IR to the Tricritical Ising Model (TIM); the theory spontaneously breaks the DOUBLE-STRUCK CAPITAL Z(2) symmetry on one side of this phase transition, and breaks SUSY on the other side. We calculate the spectrum of energies as a function of (g) over bar and see the gap close as the critical point is approached, and numerically read off the critical exponent nu in TIM. Beyond the critical point, the gap remains nearly zero, in agreement with the expectation of a massless Goldstino. We also study spectral functions of local operators on both sides of the phase transition and compare to analytic predictions where possible. In particular, we use the Zamolodchikov C-function to map the entire phase diagram of the theory. Crucial to this analysis is the fact that our truncation is able to preserve supersymmetry sufficiently to avoid any additional fine tuning.