What would be an equivalent expression to the Spanish "cortar por lo sano", probably something like "cutting by the healthy part", to convey the idea that to solve a problem from spreading, like gangrene, sometimes the solution chosen is to cut deep even through the healthy parts of the limb.
Learn English – Equivalent expression to Spanish “cutting by the healthy part”
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I'm not sure it fits exactly, but there is a phrase with similar intent in the medical profession: "life over limb". It directly mirrors your gangrene example because you might have to sacrifice part of a healthy limb to save the patient's life.
It is sometimes used beyond the literal meaning as well. For instance, moving a patient with a suspected neck injury might risk paralysis, but might be done anyway when the alternative is certain death. Someone might justify that decision by saying "life over limb."