Can mining trigger earthquakes?
Yep, mining can trigger earthquakes.

According to a Scientific American article:


  We've been monitoring [The Geysers] since 1975. All the earthquakes we see there are [human] induced. When they move production into a new area, earthquakes start there, and when they stop production, the earthquakes stop.


This is talking about geothermal power. They create small little fractures, which cause tiny earthquakes. They then harness this power for electricity.

Earthquakes can also be caused by coal mining and other mining, according to this study:


  Klose has identified more than 200 human-caused temblors, mostly in
  the past 60 years. "They were rare before World War II," he said.
  
  Most were caused by mining, he said, but nearly a third came from
  reservoir construction.
  
  Oil and gas production can also trigger earthquakes, he added.
  
  Three of the biggest human-caused earthquakes of all time, he pointed
  out, occurred in Uzbekistan's Gazli natural gas field between 1976 and
  1984 (map of Uzbekistan).


Another study also concluded this.