Synthetic protein-level circuits could enable engineering of powerful new cellular behaviors. Rational protein circuit design would be facilitated by a composable protein-protein regulation system in which individual protein components can regulate one another to create a variety of different circuit architectures. In this study, we show that engineered viral proteases can function as composable protein components, which can together implement a broad variety of circuit-level functions in mammalian cells. In this system, termed CHOMP (circuits of hacked orthogonal modular proteases), input proteases dock with and cleave target proteases to inhibit their function. These components can be connected to generate regulatory cascades, binary logic gates, and dynamic analog signal-processing functions. To demonstrate the utility of this system, we rationally designed a circuit that induces cell death in response to upstream activators of the Ras oncogene. Because CHOMP circuits can perform complex functions yet be encoded as single transcripts and delivered without genomic integration, they offer a scalable platform to facilitate protein circuit engineering for biotechnological applications.