Is it permissible for a student living in a European country, who receives a monthly salary from the state originating from mixed taxes (halal and haram), to invest his surplus money?

If you are eligible for the aid provided by the state and meet its conditions, then there is no harm in benefiting from it, even if it exceeds your needs. You can invest the surplus as long as the state does not stipulate its return. It does not matter that some of the tax money contributed by workers comes from unlawful sources.