Newton's law: A body in motion stays in motion unless acted upon by on outside force.

This largely depends on where you are in space but there is always an outside force which is some body with gravity.

If you are near a significant body of some kind (moon, planet, star) the frisbee is going to be influenced by the gravity of that object. Technically its going to influenced by your own gravity but you can through it hard enough to overcome that. The frisbee is largely going to inherit your status since the energy you impart to it isn't enough to significantly change where it goes. On that large body, even an airless one its going to land maybe a long way away, but be pulled downward until it impacts because you cant toss it with enough velocity to orbit, or reach escape velocity.

If you are in orbit it will likely also remain in orbit around the same body. It retains the momentum you had plus whatever change in velocity you give it, which isn't likely enough to cause it to leave that orbit either to impact or to escape.

If you are in/near a small body like say a 1km asteroid you might be able to toss it with enough force to escape the body, but its going to go into orbit around the sun with roughly the same orbit as the body you started in/near.

If you are in deep space, lightyears from any body yes its going to go in a straight line as far as you can tell but you are likely in orbit around the center of the galaxy so it will be too. Its just going to be in a big circle one that takes 226 million years to complete.