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.
- お金のためだと割り切って嫌な仕事をする
to do an unpleasing job convincing oneself that it's just for money
- 割り切れない気持ち
complicated feelings, feelings not logically describable
- 割り切ってしまえばホームレス生活も悪くない。
Life on the streets is not that bad once you've stopped worrying about it.
- 過去は過去だと割り切りましょう。
Don't let your past determine your present.
- 人生には割り切りも必要だ。
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.