There are a set amount of randomly generated asteroids in the game. To remove an asteroid and spawn a new one, you must mine an asteroid completely out. Asteroids vary in size and in the amounts and types of ores. To use fewer turns mining an asteroid, increase the level and type of mining bay on your vessels.
Currently there are 25 small sized asteroids (up to 1000 size) within planetary systems. When you mine one out, another small asteroid will respawn in a new planetary system.
Then there are 100 medium sized asteroids that spawn can spawn anywhere in the Expanses. When you mine out one of these, another medium roid will spawn anywhere in the expanses.
Finally there are 2 mega asteroids that can spawn anywhere in the expanses, ranging in size from 80k-110k.