The Interface Hypothesis proposes that second language (L2) learners, even at highly proficient levels, often fail to integrate information at the external interfaces where grammar interacts with other cognitive systems. While much early L2 work has focused on the syntax-discourse interface or scalar implicatures at the semantics-pragmatics interface, the present article adds to this line of research by exploring another understudied phenomenon at the semantics-pragmatics interface, namely, presuppositions. Furthermore, this study explores both inference computation and suspension via a covered-box picture-selection task. Specifically, this study investigates the interpretation of the presupposition trigger "stop" and "stop" under negation. The results from 38 native English speakers and 41 first language (L1) Mandarin Chinese learners of English indicated similar response patterns between native and L2 groups in computing presuppositions but not in suspending presuppositions. That is, L2 learners were less likely to suspend presuppositions than native speakers. This study contributes to a more precise understanding of L2 acquisition at the external interface level, as well as computation and suspension of pragmatic inferences.