Engineered genetic circuits for mammalian cells often require extensive fine-tuning to perform as intended. We present a robust, general, scalable system, called 'Boolean logic and arithmetic through DNA excision' (BLADE), to engineer genetic circuits with multiple inputs and outputs in mammalian cells with minimal optimization. The reliability of BLADE arises from its reliance on recombinases under the control of a single promoter, which integrates circuit signals on a single transcriptional layer. We used BLADE to build 113 circuits in human embryonic kidney and Jurkat T cells and devised a quantitative, vector-proximity metric to evaluate their performance. Of 113 circuits analyzed, 109 functioned (96.5%) as intended without optimization. The circuits, which are available through Addgene, include a 3-input, two-output full adder; a 6-input, one-output Boolean logic look-up table; circuits with small-molecule-inducible control; and circuits that incorporate CRISPR-Cas9 to regulate endogenous genes. BLADE enables execution of sophisticated cellular computation in mammalian cells, with applications in cell and tissue engineering.