Edit from future:
Sudden removal of sun causes space-time distortion with infinite amplitude of gravitational shock-wave. This wave would evaporate all celestial objects in the universe. Technically it's not possible. It violates "General Theory of Relativity" Following post is belong to my ignorant past. I will not delete.
The common mass center of Earth-Moon couple is about 4600km away from Earth's center. Earth's orbit around the sun is not a perfect ellipse. Earth is also moving around the earth-moon couple's center of mass like moon. Imagine an ellipse superposed with a little wave.
Vs: Earth's linear speed around sun (about 30 km/s)
Vm: Earth's linear speed around the earth-moon common mass center. (about 0.0111km/s)
Sudden removal of moon changes the orbit of earth around the sun because of Vm, not for mass removal. The distance of earth from sun is free from Earth's mass, but related with Earth's speed.
Moon-Earth orbital plane is tilting about 5 degree to Earth-Sun orbital plane. If my instincts does not fault me, the orbit of earth around the sun is forced to be a little parabolic and orbital plane changes.
On the other side the rotation speed of earth around itself does not change.