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In this paper, we consider two-dimensional N=(4,4) supersymmetric Yang-Mills(SYM) theory and deform it by a mass parameter M with keeping all supercharges.We further add another mass parameter m in a manner to respect two of the eightsupercharges and put the deformed theory on a two-dimensional square lattice,on which the two supercharges are exactly preserved. The flat directions ofscalar fields are stabilized due to the mass deformations, which gives discreteminima representing fuzzy spheres. We show in the perturbation theory that thelattice continuum limit can be taken without any fine tuning. Around thetrivial minimum, this lattice theory serves as a non-perturbative definition oftwo-dimensional N=(4,4) SYM theory. We also discuss that the same latticetheory realizes four-dimensional N = 2 U(k) SYM on R^2 x (Fuzzy R^2) around theminimum of k-coincident fuzzy spheres.

Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges