Catalyzes the transfer of a methyl group from AdoMet to trivalent arsenicals producing methylated and dimethylated arsenicals. It methylates arsenite to form methylarsonate, Me-AsO(3)H(2), which is reduced by methylarsonate reductase to methylarsonite, Me-As(OH)2. Methylarsonite is also a substrate and it is converted into the much less toxic compound dimethylarsinate (cacodylate), Me(2)As(O)-OH. [thioredoxin]-dithiol + arsenic triglutathione + 2 H2O + S-adenosyl-L-methionine = [thioredoxin]-disulfide + 3 glutathione + H(+) + methylarsonous acid + S-adenosyl-L-homocysteine 2 [thioredoxin]-dithiol + arsenic triglutathione + H2O + 2 S-adenosyl-L-methionine = 2 [thioredoxin]-disulfide + dimethylarsinous acid + 3 glutathione + 2 H(+) + 2 S-adenosyl-L-homocysteine 3 [thioredoxin]-dithiol + arsenic triglutathione + 3 S-adenosyl-L-methionine = 3 [thioredoxin]-disulfide + 3 glutathione + 3 H(+) + 3 S-adenosyl-L-homocysteine + trimethylarsine Belongs to the methyltransferase superfamily. Arsenite methyltransferase family.