Recent work in the tropics has advanced our understanding of the local impacts of land-use change on species richness. However, we still have a limited ability to make predictions about species abundances, especially in heterogeneous landscapes. Species abundances directly affect the functioning of an ecosystem and its conservation value. We applied a hierarchical model to camera- and live-trapping data from a region in Borneo, and estimated the relative abundance (controlling for imperfect detection) of 57 terrestrial mammal species, as a function of either categorical or continuous metrics of land-use change. We found that mean relative abundance increased (by 28%) from old-growth to logged forest, but declined substantially (by 47%) in oil palm plantations compared to forest. Abundance responses to above-ground live tree biomass (a continuous measure of local logging intensity) were negative overall, whilst they were strongly positive for landscape forest cover. From old-growth to logged forest, small mammals increased in their relative abundance proportionately much more than large mammals (169% compared to 13%). Similarly, omnivores and insectivores increased more than other trophic guilds (carnivores, herbivores and frugivores). From forest to oil palm, species of high conservation concern fared especially poorly (declining by 84%). Invasive species relative abundance consistently increased along the gradient of land-use intensity. Changes in relative abundance across nine functional effects groups based on diet were minimal from old-growth to logged forest, but in oil palm only the vertebrate predation function was maintained. Our results show that, in the absence of hunting, even the most intensively logged forests can conserve the abundance and functional effects of mammals. Recent pledges made by companies to support the protection of High Carbon Stock logged forest could therefore yield substantial conservation benefits. Within oil palm, our results support the view that “wildlife-friendly” practices offer a low potential for reducing biodiversity impacts.