Sorry if this has been discussed before. I searched the forums but couldn't find a proper answer.

Grudge Thrower Assault (bold text mine)

"Play during combat, after damage has been assigned .
Action: Destroy one target attacking unit."

Here's my question:
What happens with the damage assigned by the destroyed unit ? Is it canceled or it is applied normally ?

It's appplied normally. The unit's damage has been assigned, therefore it's stays. Destroying the unit at that time during the turn will not cancel any damage.