We used horn measurements from natural and hunted mortalities of male thinhorn sheep Ovis dalli from Yukon Territory, Canada, to examine the relationship between rapid growth early in life and longevity. We found that rapid growth was associated with reduced longevity for sheep aged 5 years and older for both the hunted and natural mortality data sets. The negative relationship between growth rate and longevity in hunted sheep can at least partially be explained by morphologically biased hunting regulations. The same trend was evident from natural mortalities from populations that were not hunted or underwent very limited hunting, suggesting a naturally imposed mortality cost directly or indirectly associated with rapid growth. Age and growth rate were both positively associated with horn size at death for both data sets, however of the two growth rate appeared to be a better predictor. Large horn size can be achieved both by individuals that grow horns rapidly and by those that have greater longevity, and the trade‐off between growth rate and longevity could limit horn size evolution in this species. The similarity in the relationship between growth rate and longevity for hunted and natural mortalities suggests that horn growth rate should not respond to artificial selection. Our study highlights the need for the existence and study of protected populations to properly assess the impacts of selective harvesting.