In Legends, Yes (although they can be reconnected)
In Legends continuity, there are several cases of cutting oneself off from the Force, but in all of them, it was later restored.
Meetra Surik ("The Jedi Exile")
The protagonist of Knights of the Old Republic II: The Sith Lords instinctually cut herself off from the Force to survive the devastation that occurred on Malachor V which turned the place into a Wound in the Force.
Vrook: We did not cut you off from the Force. You were merely deafened to it, because of that last battle of the Mandalorian Wars. [...]
Kavar: It was too much for any Jedi to endure... and it is a wonder that you did not die there when thousands perished, all those you and fought with and struggled with. You cut yourself off, because you had to if you were to survive.
She later recovered her connection to the Force over time, and retraining her Jedi skills.
The opening crawl of Jedi Knight II: Jedi Outcast says this:
After defending the VALLEY OF THE JEDI from the evil JEREC and nearly falling to the Dark Side himself, former Jedi Knight KYLE KATARN has severed his connection with the Force and returned to his mercenary ways.
The mechanics of how he severed his connection with the Force aren't elaborated on, but he reconnects with the Force when he goes to the Valley of the Jedi, a powerful nexus of the Force. So either it was involved in severing his connection, or he did something else to deaden his connection. Either way, midichlorians weren't involved.
While not completely cut off from the Force, Cade Skywalker, descendant of Luke Skywalker, used death sticks to temporarily cut off his connection with the Force.
Luke Skywalker (Force Ghost): Why do you use those death sticks?
Cade Skywalker: They keep you away.
Luke: They also deaden your connection to the Force.
Cade: Point two in their favor!
He later recovered by stopping the use of Death Sticks and embracing his Jedi identity.