If an (for example "Leather Tunic") with the Attribute attackDamage,Operation:0,-1 is equipped, you cant deal Damage to Mobs.
But if you get a Sword with (for Example attackDamage,Operation:0,2 you hurt the Mobs with Atk Damage 2.

Now. If you deselect the Sword with attackDamage,Operation:0,2 you deal normal Damage to Mobs, and not 0.

Commands Used:

/give @p leather_chestplate 1 0 {AttributeModifiers:[{Operation:0,UUIDLeast:1,UUIDMost:1,Amount:-1,AttributeName:generic.attackDamage,Name:tunic}]}
/give @p iron_sword 1 0 {AttributeModifiers:[{Operation:0,UUIDLeast:1,UUIDMost:1,Amount:2,AttributeName:generic.attackDamage,Name:sword}]}