Just because a type is super effective against another, doesn't mean it also has a resistance in return. In fact there are quite a lot of types like this. As an example, Bug is Super Effective against both Psychic and Dark. But Bug type does not have a resistance to Psychic or Dark. The opposite is also true -- there are types that resist others, without being Super Effective against them in return. Fire is resistant to Fairy, but is not Super Effective against it.
In the case of Aurorus, it is both Ice and Rock types. Ice may be Super Effective against Grass, but it provides no defense against Grass (or anything, really, except other Ice types -- defensively, Ice is the weakest typing possible). Similarly, Ground is Super Effective against Rock. Even though Ice is Super Effective against Rock, it again does not provide any defense against Rock.