Either is correct:

...cut what is between X and Y.

or

...cut what is in between X and Y.

There are no set guidelines or even prejudices that I am aware of with regard to the choice between "between" and "in between." They are perfectly common synonyms that are used interchangeably according to sense, feel, rhythm, and whatever else informs these kinds of language decisions.

The prepositional form is always two separate words, "in between." Thus:

"Cut what's in between"

The adjectival/nominative form of the combination is still hyphenated by all the dictionaries I see, that is "in-between," meaning intermediate, as in:

Method X is an in-between solution; it will not be satisfactory for the long term."

The adverbial form is explained in the section heading of the OED with this parenthetical remark: "(Mostly the preposition with object understood)." Examples of adverbial uses would include:

I stood at the edge, pondering the emptiness between.
The two fighters reconverged on each other, but the referee rushed between.
The sale was nearly closed, and then Sylvia got between.