IMO, a pure language would be one which is incapable of representing impure code. Or at least, where it's very hard. I don't know where the line lies, but I strongly feel that any language that supports manual memory management, pointers, and mutable variables can't properly be called "pure".

Some people get confused between purity and expressiveness. Inexpressive languages like C require using impure constructs to represent fundamentally pure constructs. More expressive languages like Python don't need as many impure workarounds. Haskell, as a very expressive language, can do amazing things in pure code that other languages must resort to impurity for.

If you want a pure language, look into Agda or Coq.