apotomos describes a severe or sharp manner of rebuke or dealing in the two cited passages.

The two occurrences show the adverb marking a severe manner in corrective action: anticipated dealing in 2 Corinthians 13:10 and direct rebuke in Titus 1:13.

1. Severe manner in correction · dominant

   In 2 Corinthians 13:10, the adverb modifies the anticipated manner of dealing when present, set against authority for building up rather than tearing down; the APB renders the clause "I may not deal severely." In Titus 1:13, it modifies the command to rebuke, followed by the aim that they may be sound in the faith; the APB renders "rebuke them sharply."

   2 Corinthians 13:10Titus 1:13

In the Anselm Project Bible: The APB presents the adverb with "severely" in 2 Corinthians 13:10 and "sharply" in Titus 1:13. These renderings confirm the corrective force of the clauses rather than establish separate senses.