Asking about the exact number of squares in the beginning and at the end is a red herring.
Assume that a square on the board is one unit in length, and one in width. Then, the original board has 8*8 units = 64 units squared.
After the cut, the board can be seen as being two 7*8 right triangles, and one 1*8 strip of squares.
(1/2)(7*8) units +(1/2)(7*8) units + (1)(8) units = 64 units squared.
It's just a peculiarity of the slope that our chainsaw artist chose that the board appears to have 'lost' squares. It appears to have lost an intact square, but all the area is still there, and the Universe is still safe.