You can write a swap function using Array2D.mapi that doesn't mutate the original array. This will return a new array with the swapped values:
let swap (arr : int[,]) i1 i2 =
let map i j v =
match (i,j) with
| t when t = i1 -> arr.[fst i2, snd i2]
| u when u = i2 -> arr.[fst i1, snd i1]
| _ -> v
arr |> Array2D.mapi map