We study the lattice model for the supersymmetric Yang-Mills theory in two-dimensions proposed by Cohen, Kaplan, Katz, and Unsal. We re-examine the formal proof for the absence of susy-breaking counterterms as well as the stability of the vacuum by an explicit perturbative calculation for the case of $U(2)$ gauge group. Introducing fermion masses and treating the bosonic zero momentum mode nonperturbatively, we avoid the infra-red divergences in the perturbative calculation. As a result, we find that there appear mass counterterms for finite volume which vanish in the infinite volume limit so that the theory needs no fine-tuning. We also find that the supersymmetry plays an important role in stabilizing the lattice spacetime by the deconstruction.