Domesticated strains of Saccharomyces cerevisiae have adapted to resist copper and sulfite, two chemical stressors commonly used in winemaking. S. paradoxus has not adapted to these chemicals despite being consistently present in sympatry with S. cerevisiae in vineyards. This contrast could be driven by a number of factors including niche differences or differential access to resistance mutations between species. In this study, we used a comparative mutagenesis approach to test whether S. paradoxus is mutationally constrained with respect to acquiring greater copper and sulfite resistance. For both species, we assayed the rate, effect size, and pleiotropic costs of resistance mutations and sequenced a subset of 150 mutants. We found that the distributions of mutational effects displayed by the two species were similar and poorly explained the natural pattern. We also found that chromosome VIII aneuploidy and loss of function mutations in PMA1 confer copper resistance in both species, whereas loss of function mutations in REG1 were only a viable route to copper resistance in S. cerevisiae. We also observed a de novo duplication of the CUP1 gene in S. paradoxus but not in S. cerevisiae. For sulfite, loss of function mutations in RTS1 and KSP1 confer resistance in both species, but mutations in RTS1 have larger effects in S. paradoxus. Our results show that even when available mutations are largely similar, species can differ in the adaptive paths available to them. They also demonstrate that assays of the distribution of mutational effects may lack predictive insight concerning adaptive outcomes.