Looking at a new weapon, in defense, it has a minus HP. Does it mean that when my pet uses that weapon, it will loose HP?

You got it - it'll lose HP. What weapon are you looking at?

Thank you for the answer! I guess it's not worth it then.

Sometimes it can be worth it! Usually weapons with a negative heal give you extra attack power. For example, Shriek of Despair Scroll heals you -3% each time you use it, but it is one of the best scrolls in the game due to its high freezing rate. The negative heal helps strong weapons stay balanced.