When the Digger prepares an attack, it places a rock on any empty adjacent tiles. The rocks each have 1 health. When the digger executes its attack, it deals 1 damage to every adjacent tile.
It is typically best to dispatch Diggers using ranged artillery strikes or other abilities which are capable of bypassing the Digger's protective rock obstacles. If your squad lacks any such abilities, Diggers are likely the most dangerous non-alpha Vek you can encounter, and you may want to avoid traveling to islands with Diggers until your squad obtains a wider variety of weapons.
It is possible to destroy a Digger with a single melee/push-oriented Mech (provided it is capable of doing 2 damage, or 1 + push), but some set-up is required. You should try to position your Mech in a position where it will be adjacent to the Digger when the Digger targets its next attack. Stand next to a grid building that the Digger is likely to target, or force the Digger to attack your Mech by blocking its path to any possible targets other than your Mech. The Digger won't be able to create a rock where your Mech is standing, and you will be able to attack it.