It could be a wall-hanger piece meant to show off, not necessarily to fight with.

However, while rapiers may have been thrust-centric weapons, they weren't thrust-only weapons, and treatises do show cutting techniques. There are rapiers with really thin blades that pretty much can't cut, but there are also ones with somewhat wider blades which can - not as effectively as arming swords or sabers of course, but still, they can cut.

here's a scholagladiatoria video talking a bit about rapiers' cutting ability - Rapiers CAN Cut. Or Can they?