This might be the most obvious answer but the ISS would fly off into space. Why? Well to keep it simple the ISS is continuously falling toward the earth but it is just going fast enough that it more or less falls "around" the earth.
How Do Satellites Get & Stay in Orbit?
To keep doing that the ISS and all objects in orbit around the earth (or any other celestial body) has to have a lot of momentum, which means that when the Earth disappeared the gravity that anchored the ISS to the Earth disappeared with it making the ISS fly off into space.
This on its own probably did not kill the astronauts (assuming they did not crash into something) but eventually they probably ran out of food. I have heard that the ISS can survive for around half a year on its own so they probably just shot off to somewhere else. How Long Can The ISS Survive Without New Supplies?
But I do feel bad about those astronauts, Earth disappeared, their home gone and now they are alone, in space, with no home to return to waiting out their days till their inevitable death.