Yes, human usage of some resources can be responsible for natural calamities. For example, over use of coal and the draining of underwater lakes can cause sinkholes. The over use of wood can lead to deforestation that can cause tornadoes due to the wind and storm fronts no longer having the forest to buffer them.
When speaking about natural calamities from resource use, several come to mind. The gulf oil spill is one specific event, and global warming is a very broad yet very dangerous one. When we search for resources, we usually end up tearing apart the planet. Fracking is another one that can cause calamities of the environment too.