Effective turnover of many incorrectly processed RNAs in yeast, including hypomodified tRNAiMet, requires the TRAMP complex, which appends a short poly(A) tail to RNA designated for decay. The poly(A) tail stimulates degradation by the exosome. The TRAMP complex contains the poly(A) polymerase Trf4p, the RNA-binding protein Air2p, and the DExH RNA helicase Mtr4p. The role of Mtr4p in RNA degradation processes involving the TRAMP complex has been unclear. Here we show through a genetic analysis that MTR4 is required for degradation but not for polyadenylation of hypomodified tRNAiMet. A suppressor of the trm6-504 mutation in the tRNA m1A58 methyltransferase (Trm6p/Trm61p), which causes a reduced level of tRNAiMet, was mapped to MTR4. This mtr4-20 mutation changed a single amino acid in the conserved helicase motif VI of Mtr4p. The mutation stabilizes hypomodified tRNAiMet in vivo but has no effect on TRAMP complex stability or polyadenylation activity in vivo or in vitro. We further show that purified recombinant Mtr4p displays RNA-dependent ATPase activity and unwinds RNA duplexes with a 3′-to-5′ polarity in an ATP-dependent fashion. Unwinding and RNA-stimulated ATPase activities are strongly reduced in the recombinant mutant Mtr4-20p, suggesting that these activities of Mtr4p are critical for degradation of polyadenylated hypomodified tRNAiMet.