I had the same issue, but I was able to destroy the chair by shooting at it. The first time I used Destiny III and it blows additionally the ground so that the mission fails. The second time I do it with a sniper rifle (+ Sneak Attack, so 240 damage, I don’t know if normal damage is enough to destroy it) and this time it destroyed only the chair. The tile with the objective was free and I was able to end the mission successful.
So don’t use burst weapons or explosives, I think Hell II would be the best solution, and aim careful so that you not shot the ground.