I am tiling a bedroom floor with 20" tile on the diagonal. Is there a way to layout the tile so as to minimize cutting? I am fine with trying the layout in reality and making adjustments to it as needed. I can also work with graph paper.
No, there isn't. You'll want to follow a common strategy of either running a full tile or a joint down the center of the room so that the rows at the edges look appropriate. Snap one or two chalk lines on the floor as references, then snap one or two at 90 degrees to get your joint lines straight.
With a wet saw these types of cuts are not difficult nor time consuming. With a helper you can lay tile almost as fast as you can mark the cuts. Once you work out a strategy for measuring it's easy.
with tiles aligned diagonally every edge tile will need to be cut. Arrange the layout for best look.
A 45 degree diagonal layout reduces wastage because the offcut can be used in the next place along (unless you are doing two-colour tiling, or have tiles with a directional pattern) it also hides crooked walls
Draw up the room outline to scale on transparent sheet and place it over a scale representation of the tile grid. Once it looks good staple it in place.
Try to avoid any layout that requires cutting the tips off tile corners, cutting one third to one half off is easier and looks better.