to mine subsurface resources you need to find a subsurface source, target one of the location on the asteroid highlighted by an icon and it will show as either surface, subsurface or fissure
youll need to target one of the subsurface resources then fire a displacement missile at the target whilst keeping the fire button depressed. the missile will then either burrow into the rock if its on target or bounce off if it misses
if the resource is identified as a surface resource you will need to use an abrasion blaster to chip off the rock
if the asteroid has "core detected" then youll need to fire seismic charges into the fissures until you hit an optimal yield before it detonates - or manual detonation