Irreversible logic is at odds with unitary quantum evolution. Emulating such operations by classical measurements can result in disturbances and high resource demands. To overcome these limitations, we propose protocols that harness dissipation to realize the nonunitary evolution required for irreversible gate operations. Using additional excited states subject to decay, we engineer effective decay processes that perform the desired gate operations on the smallest stable Hilbert space. These operate deterministically and in an autonomous fashion, without the need for measurements. We exemplify our approach considering several classical logic operations, such as the OR, NOR, and XOR gates. Towards experimental realization, we discuss a possible implementation in quantum dots. Our study shows that irreversible logic operations can be efficiently performed on realistic quantum systems and that dissipation engineering is an essential tool for obtaining nonunitary evolutions. The proposed operations expand the quantum engineers' toolbox and have promising applications in NISQ algorithms and quantum machine learning.