Doing it using the method you describe, will always cut off the points in the next round. To avoid losing your points, you need to have larger yellow triangles. If you use a large yellow square and cut on both diagonals, you will be sewing a straight grain to the straight grain of your blue square, but then have bias edges left on the outsides.
Instead, consider using HST's So, blue square = 4", cut two yellow squares a minimum of 4 7/8" (but I use 5", then trim to size later) Cut each yellow square in half diagonally and sew to blue square (opposite sides first, then the other two sides). Trim, making sure you leave 1/4" at each point to allow for seams. Using the HST's, you will be sewing a bias onto your straight grain edge, which will leave you with two straight grain edges on the outside. Does that make sense?