Multi-photon dissipation – a key resource for bosonic qubits – is usually realized by parametrically pumping a Josephson coupler at the cost of spurious nonlinear terms. Here we instead engineer it using a dc-voltage-biased SQUID, such that these parasitic terms average out. We activate the conversion of one, two, or four photons of a high-Q mode into a single photon of a lossy mode. We characterize the two-photon dissipation by Wigner tomography, establishing dc-biased junctions as a resource for reservoir engineering and a viable route to cat-qubit stabilization.