The murder is committed on US soil. the fugitive flees to Canada. The US requests Canada arrest the fugitive, which they do. US requests extradition. Canada refuses because US has capital punishment. Does Canada now try the fugitive for murder in Canada or is the fugitive simply released?
Absent exceptional circumstances like war crimes, Canada would not try the suspect for murder. It might incarcerate the suspect, however, while engaging in negotiations with U.S. officials to try the defendant for murder in a state court or federal court with jurisdiction over the case and an agreement not to seek the death penalty.