The 3' to 5' exonuclease Pop2p (Caf1p) is part of the CCR4-NOT deadenylation complex that removes poly(A) tails from mRNAs in cells. Pop2p is structurally conserved in eukaryotes, but Pop2p harbors noncanonical amino acids in its catalytic center. The enzymatic properties of Pop2p are not well defined. Here we characterize the RNA exonuclease activity of recombinant Pop2p. We find that Pop2p degrades RNAs via two alternative reactions pathways, one generating nucleotides with 5'-phosphates and RNA intermediates with 3'-hydroxyls, and the other generating nucleotides with 3'-phosphates and RNA intermediates with 3'-phosphates. The enzyme is not able to initiate the reaction on RNAs with a 3'-phosphate, which leads to accumulation of RNAs with 3'-phosphates that can exceed 10 nt and are resistant to further degradation by Pop2p. We further demonstrate that Pop2p degrades RNAs in three reaction phases: an initial distributive phase, a second processive phase and a third phase during which processivity gradually declines. We also show that mutations of subsets of amino acids in the catalytic center, including those previously thought to inactivate the enzyme, moderately reduce, but not eliminate activity. Only mutation of all five amino acids in the catalytic center diminishes activity of Pop2p to background levels. Collectively, our results reveal robust exonuclease activity of Pop2p with unusual enzymatic properties, characterized by alternative degradation pathways, multiple reaction phases and functional redundancy of amino acids in the catalytic core.