Congenital amusia is a neuro-developmental disorder of pitch perception that causes severe problems with music processing but only subtle difficulties in speech processing. This study investigated speech processing in a group of Mandarin speakers with congenital amusia. Thirteen Mandarin amusics and thirteen matched controls participated in a set of tone and intonation perception tasks and two pitch threshold tasks. Compared with controls, amusics showed impaired performance on word discrimination in natural speech and their gliding tone analogs. They also performed worse than controls on discriminating gliding tone sequences derived from statements and questions, and showed elevated thresholds for pitch change detection and pitch direction discrimination. However, they performed as well as controls on word identification, and on statement-question identification and discrimination in natural speech. Overall, tasks that involved multiple acoustic cues to communicative meaning were not impacted by amusia. Only when the tasks relied mainly on pitch sensitivity did amusics show impaired performance compared to controls. These findings help explain why amusia only affects speech processing in subtle ways. Further studies on a larger sample of Mandarin amusics and on amusics of other language backgrounds are needed to consolidate these results.