The literal and basic meaning of 割り切る is "to (cleanly) divide", as in 10は2と5で割り切れる (="Ten is evenly divisible by 2 and 5."). Another meaning of this verb is related to this but is rather nuanced. It's something like "to take it as-is without worrying too much", "to make a decision anyway ignoring trivial things", "to (forcibly) convince oneself", etc.
to do an unpleasing job convincing oneself that it's just for money
complicated feelings, feelings not logically describable
Life on the streets is not that bad once you've stopped worrying about it.
Don't let your past determine your present.
Sometimes it's necessary to make a practical decision ignoring something.
I think definitions on jisho.org are not really spot-on. I could not find satisfactory definitions/translations even in other dictionaries, so the translations above are largely based on my own understanding.
In your example, 浮気と割り切る probably means "to take it merely as a cheating" or "to have no illusion about cheating", implying the other person is not going to cross a line and break the marital relationship.