The fission yeast telomerase RNA (TER1) precursor harbors an intron immediately downstream from its mature 3' end. Unlike most introns, which are removed from precursor RNAs by the spliceosome in two sequential but tightly coupled transesterification reactions, TER1 only undergoes the first cleavage reaction during telomerase RNA maturation. The mechanism underlying spliceosome-mediated 3' end processing has remained unclear. We now demonstrate that a strong branch site (BS), a long distance to the 3' splice site (3' SS), and a weak polypyrimidine (Py) tract act synergistically to attenuate the transition from the first to the second step of splicing. The observation that a strong BS antagonizes the second step of splicing in the context of TER1 suggests that the BS-U2 snRNA interaction is disrupted after the first step and thus much earlier than previously thought. The slow transition from first to second step triggers the Prp22 DExD/H-box helicase-dependent rejection of the cleaved products and Prp43-dependent "discard" of the splicing intermediates. Our findings explain how the spliceosome can function in 3' end processing and provide new insights into the mechanism of splicing.