No – this would violate Liskov’s Substitution Principle. You should always be able to use an instance of a subtype as if it were an instance of a supertype.
Don’t forget that a caller may only be aware of your type “as” the base type or an interface. Consider this code:
object foo = new TypeWithToStringRemoved();
foo.ToString();
That would have to compile, wouldn’t it? Now what would you expect to happen at execution time?
Now for ToString, GetHashCode, Equals and GetType there’s no way to avoid having them in the first place – but usually if there are methods you want to “remove” from a base type, that suggests you shouldn’t be inheriting from it in the first place. Personally I find the role of inheritance is somewhat overplayed in object oriented programming: where it’s useful it’s really useful, but generally I prefer composition over inheritance, and interfaces as a form of abstraction rather than base classes.