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No, cutting the cable won't kill you.. as long as you don't short out the battery in the process. If there's enough slack in the cable, a new end can be attached, so you may not need to replace it -- usually much easier to do in cold weather. Autozone should have a selection.
Incidently, the corroded cable may be the problem with your battery or contributing to it. So, also get a cable clamp cleaner and clean the mating surfaces of battery & cable for both cables. You want bright shiny metal on both contacting surfaces. Slather the cable with grease after attaching to keep the future corrosion problem down (I've used everything from axel grease to vaseline, whatever was handy).
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