TL:DR: We don't know if anyone is still mining, however, we can speculate.
I've just re-watched the entire Jon leaving Dragonstone scene and I can confirm we see no one mining away.
However, Jon is a smart guy and Dargonglass is now the most valuable resource in Westeros. It would make sense for there to still be people mining away. But it wouldn't make sense for him to leave his own men. He already doesn't have enough to hold the wall and should Dany change her mind she can then take his men captive. Therefore, I doubt that he would have left some of his own men.
Dany has a massive army and most of the Dothraki appear to still be at Dragonstone. It makes more sense for Jon's men to have shown the Dothraki what to do and have them mine it out.
The following scene and this script seem to back up this idea:
"I will allow you to mine the dragonglass and forge weapons from it. Any resources or men you need, I will provide for you."
Though it isn't conclusive either way.
On the other hand, Jon knows it is a valuable resource and needs it across the North as quickly as possible. he could have left some skilled men down in the mines to have the process go faster.