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Topological Dirac and Weyl semimetals are currently attracting intense interest due to their exotic physical properties. Transition metal diarsenides such as MoAs_{2} and WAs_{2} have been reported to harbor very high magnetoresistance suggesting the possible existence of a topological quantum state, although this conclusion remains dubious. Here, using systematic angle-resolved photoemission spectroscopy (ARPES) measurements and parallel first-principles calculations, we discuss the electronic structures of TAs_{2} (T = Mo, W). Two different cleavage planes of MoAs_{2} are found to harbor distinctly different surface states. Our experiments show the presence of Dirac-like dispersions on the (001) plane, which our first-principles calculations ascribe to trivial surface states. Our in-depth study also finds WAs_{2} to possess a trivial electronic structure. Our study emphasizes the importance of identifying the cleavage plane in low-symmetry systems and indicates that topological semimetallic states are not the key for generating high magnetoresistance in MoAs_{2} and WAs_{2}.