Theresa, moles do not eat or shred plants. They eat insects that are in the soil. Sometimes their tunneling is destructive, though.
The best way I've found to make them move somewhere else is to simply flood the tunnels with the hose whenever I am out in the garden.
No chemicals, no traps, no mole murdering. They do serve a purpose to rid the garden of grubs and other plant destroying bugs. If you have a natural (non chemical) garden, you have all kinds of bugs, both good and bad, so the moles are going to be attracted to your garden.
But if you consistently flood their tunnels for a week or two they will decide there must be a better place to live.
