This is called 鯉口を切る. In some monolingual dictionaries, there is even an entry for it:
Source: 大辞泉 via kotobank.jp
the description roughly translating to
Pulling out the blade a little bit so as to enable quick drawing of the sword. Loosening the mouth of a sword sheath.
鯉口 koiguchi literally means "carp's mouth", because, well, the mouth of the sheath resembles an open carp's mouth.
The verb 切る kiru has many different meanings (大辞泉 lists 22 meanings) and here 切る should maybe not be understood with its common meaning of "cutting" but probably with the meaning of "opening something sealed/closed" (point 3 in ibid.).