The existing answer correctly identifies the meaning of "wipe", but to truly understand Hermione's intent I think you need to look at the context. In this conversation they are talking about Quidditch, a game played 50+ feet in the air on flying broomsticks. If you recall from earlier in the book, the last time Harry played Quidditch his broomstick malfunctioned and he was nearly thrown off. In fact, at this point in the story they suspect that the broomstick malfunctioned because of Snape.
In this conversation they are worrying that the same thing might happen again, especially because Snape is going to be refereeing the game (giving him the opportunity to tamper with Harry's broomstick again). So in the context of this conversation, Hermione is most likely referring to the possibility of Harry falling off of his broomstick. When a person falls to the ground from a great height it is commonly described as "splattering on the ground" or something similar. That is to say that because of the tremendous force with which the body hits the ground, the body actually gets pulverized to some extent. The remains of the body would be more like a liquidy/mushy mess of blood, skin and bone than a body. Thus, Hermione is saying that she doesn't want Harry to fall which would cause them to "wipe him up" off the field much like you would wipe up an egg that fell on the floor and cracked.