un·der·mine 
(ŭn′dər-mīn)
(ŭn′dər-mīn)tr.v. un·der·mined, un·der·min·ing, un·der·mines
1. To weaken by wearing away a base or foundation: Water has undermined the stone foundations.
2. To weaken, injure, or impair, often by degrees or imperceptibly; sap: Late hours can undermine one's health.
3. To dig a mine or tunnel beneath.