'A surprise party' is an event planned in secret. The person for whom this party is planned is not expecting it to happen. This phrase is made up of two nouns - 'surprise' + 'party'. The first noun ('surprise') tells you want kind of party it is. It's the same construction grammatically as 'birthday party' or 'Christmas party'. 'Surprising' is the present participle of the verb 'to surprise', used here as an adjective. It tells you about the speaker's reaction to the party. 'A surprising party' is a party which is unusual in some way. It's the same construction grammatically as 'a boring party' or 'an interesting party'. 'Surprised party' is nonsense. Think about it. A person can be surprised, as in 'I was surprised to hear the news'. To be 'surprised' is an emotional reaction. A party can't feel emotions, so it can't be surprised, can it?

You want the first one if you're referring to a party that is unexpected by the person it is intended for. * I'm going to throw her a surprise party for her birthday. On the other hand, if you want to say that something about the party was not normal in some way a suprising party works. * That was a really surprising party. I was not expecting it to be so fun.