As I understand from your description, you use loop cut tool from toolbar:
So then you press to make a cut, not release mouse button, instead move cursor to the sides, and you will see that you are able to slide loop cut to the sides. Release button only then you like the position of the cut.
If you press E while holding the mouse button, you will see that the loop cut is parallel to one side. If that side is wrong, press F to flip the side.
Also, you can use knife tool which give more freedom in making cuts.
If you press A after adding the first point, you will be able to make perfect horizontal or vertical cuts.
Information about available keys you can see in the toolbar:
