Installing a mirror on wardrobe sliding door

I would suggest hollow wall anchors. Four of them, two per side and six to eight inches from each end. These anchors come in different grip ranges so you have to have one that is matched for the thickness of the door panel (likely 1/8") plus the wooden frame of the mirror. They can hold a reasonably good load and they have amazing pullout when used on paneling and hollow doors.

An example of the anchors is here https://www.boltdepot.com/fastener-information/Anchoring-Products/Hollow-Wall-Anchor-Info.aspx

If you don't have enough wood frame around the mirror then you may have to use a mirror clip with the hollow wall anchors.

This suggestions though will put four holes in the door skin about a 1/4" in diameter.