Minefields

This card’s Special Rule effect resolves during the Move Ship step while executing a maneuver.

The standard obstacles are used during setup, which are 3 asteroid fields, 2 debris fields, and 1 station. The second player places all obstacles, and they can be placed anywhere in the setup area (including in deployment zones) but must be placed beyond distance 5 of each other. Then the second player places 6 objective tokens in the play area, these must be placed at distance 1 of an obstacle and beyond distance 1 of all other objective tokens.

The special rule:
While a ship is executing a maneuver, if that maneuver will at “end” distance 1 of an objective token, remove that objective token from the play area and roll 2 blue die. That ship is dealt 1 damage card per hit or Critical icon rolled, if there is a critical icon showing, deal the first damage card faceup.
This damage inflicted is NOT an attack. This damage CANNOT be reduced or canceled by defense tokens, nor any card effects that involve moving or reducing damage can be utilized (unless they are effects not used in the term “attack” or otherwise stated).

A Raddus ship can be deployed on or near mines from Minefield. As deploying is not a maneuver, it is a deployment or placement. Once a ship conducts a maneuver, if it ends movement near a mine, that mine can resolve its effect. Also if a squadron with strategic moves an objective token near a ship, the special rule effect only resolves when a ship executes a maneuver. Not when an objective token is moved near it.

In regards to what happens if a ship with 1 hull overlaps another ship and would be destroyed, does it still resolve any Minefields mines it ends its maneuver near.
Short answer, yes.
Long answer to follow and it revolves around timing and current precedents.

Per the FAQ we know the following things.
First, That obstacle effects only take place after a maneuver has been executed, meaning that a ship with 1 hull cannot ram a ship, drop to 0 hull, and then land on a station,and go back up to 1 hull. Once a ship is destroyed, it cannot be “un-destroyed”
“Q: If a ship overlaps another ship and suffers damage so that it has damage cards equal to its hull value but its final position is overlapping the station obstacle, is that ship destroyed?
A: Yes. The station’s effect is not resolved until after the ship executes its maneuver.”

Second, that mines from the objective Minefields have the following FAQ:
“This card’s Special Rule effect resolves during the Move Ship step while executing a maneuver.”

Meaning that the mines from Minefields explode before a ship has ended its maneuver. This was to prevent Demolisher from attacking before being destroyed by mines.

Thus this would resolve in the following steps.
Ship with 1 hull remaining overlaps another ship, and drops back on the maneuver tool to the next available position. The ship now has 0 hull but it is not yet removed from play.
The ship is still considered “maneuvering” and checks to see if its maneuver is at Distance 1 of any mines, if so, these mines resolve their effects. Damage cards are still dealt. Any overlapped squadrons are placed.
Now the ship ends its maneuver and is removed from play before it suffers the effects of any obstacle it may of overlapped.