The word undermine is an interesting one. It current day usage, it is mostly used in the sense of weakening somebody or something in a discreet or subtle way.
We can actually break down undermine into: under+ mine, that is to mine under a place. An extension of this mining is when the base or foundation of building is word down and weakened. And another extension of the same concept is in the figurative sense: when somebody undermines someone, he is weakening his base or foundation.
The dictionary definitions for undermine are as follows:
1. To weaken by wearing away a base or foundation. (verb)
2. To weaken, injure, or impair, often by degrees or imperceptibly; sap. (verb)
3. To dig a mine or tunnel beneath. (verb)
The following is an extract used for educational purposes: ‘“Private sector demand remains fragile and access to finance continues to be constrained. The current plans for fiscal consolidation could therefore have a significant and lasting negative impact on the economy.” They argued higher unemployment, triggered by the cuts, would “undermine” Mr Osborne’s efforts to balance the books and urged him instead to pursue a strategy of promoting economic growth.’