So I was looking at conjugations and I saw that the potential form of 切る【きる】 is 切れる【きれる】. However, 切れる【きれる】 is also an intransitive verb. There are others e.g.
So, what's the difference?
Short answer: Verbs like 切れる can have two meanings, the potential one or the intransitive one. You determine by context.
In this case, it is clear the boss got mad. It could also be written as キレた.
Here, it should be clear the person is asking "Can this string be cut?". This meaning can also be written as 〜切ることができる.