Just took a look into the ini files for the minefields and at first glance (without being able to play the game at the moment) I'd say that they can't be destroyed.
They are referenced similar to Asteroids. Here's one of the INIs:
[TexturePanels
file=solar\asteroids\mine_shapes.ini
[Field
cube_size=250
fill_dist=1000
diffuse_color=110, 110, 100
ambient_color=255, 255, 255
ambient_increase=20, 20, 30
[properties
flag=mine_danger_objects
flag=danger_density_high
[Exclusion Zones
exclusion=Zone_Rh04_minefield_track1
exclusion=Zone_Rh04_minefield_track2
exclusion=Zone_Rh04_minefield_track3
exclusion=Zone_Rh04_minefield_track4
exclusion=Zone_Rh04_minefield_track5
exclusion=Zone_Rh04_minefield_track6
exclusion=Zone_Rh04_minefield_track7
exclusion=Zone_Rh04_minefield_track8
exclusion=Zone_Rh04_minefield_track9
exclusion=Zone_Rh04_minefield_track10
exclusion=Zone_Rh04_minefield_track12
exclusion=Zone_Rh04_minefield_track13
exclusion=Zone_Rh04_minefield_track14
exclusion=Zone_Rh04_minefield_track4a
exclusion=Zone_Rh04_nomad_shipyard_exclusion
[Cube
xaxis_rotation=8, 40, 90, 158
yaxis_rotation=5, 45, 100, 135
zaxis_rotation=355, 45, 78, 145
asteroid=mine_radiate, -0.9, 0, 0.05, 110, 0, 10, mine
asteroid=mine_radiate, 0.75, 0.1, 0, 0, 45, 20, mine
asteroid=mine_radiate, 0.05, -0.75, -0.1, 50, 35, 40, mine
asteroid=mine_radiate, 0, 0.85, 0.1, 150, 15, 12, mine
asteroid=mine_radiate, 0.1, 0, -0.85, 40, 0, 50, mine
asteroid=mine_radiate, -0.1, 0.05, 0.9, 30, 15, 60, mine
I'm guessing, similar to the large asteroids in the game, that they can't be destroyed...but that's a guess.
-V
The Nets Edge
Freelancer .INI File Parser
Freelancer IDSName Matcher