After cutting off the damaged terminal & stripping the cable slightly less than the depth of the replacement terminal, some corrosion within the strands is visible.

After removing any grease & oil with brake cleaner (etc.), the strands can be brushed or scraped clean. It may be necessary to flatten the bundle in various directions to expose the corrosion for thorough cleaning.

The terminal I'm using is a negative 2/0 from Carquest (BP96) and is specifically sized for the negative post (note the N debossed into it). The corresponding positive is BP95, and they were ~$7ea in 2009. The NAPA equivalents are 728014 (pos) & 728015 (neg) ~$9ea. Other sizes are available to accomodate more or less wire in the socket. They're cheaper online, but shipping must be considered.

See also:
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Motorcraft F2TZ-14301-B Negative Battery Cable with body, frame, & block grounds

Owner caption April 2009 · Photo 2523 of 5000