Use three woodworking clamps, two on one side and one on the other, to hold the joints together while the glue dries. Once again, immediately clean off any excess glue.
To ensure that the cutting board is square, measure diagonally from corner-to-corner, and then measure the opposite diagonal. If the two measurements are equal, the board is square.
By using two clamps on one side of the board and one on the opposite side, you should be able to ensure that the cutting board will be flat after the glue dries.