Yes you can mix tenses, but for a learner, you should not mix tenses. Generally, mixing tenses are not necessary and there is always a way for you to phrase a sentence without a mix of tenses.
In your scenario above, the want had originated before the sentence was said. So using past tense is proper. However, you still do want a more sophisticated method at the time you made the statement, so using 'is' is proper as well. But this sentence itself does not have a complete meaning without a given context, which is fine if it is conversational English instead written English. If you are writing something though, you should consider rephrasing it.
Some "more proper" ways to say it will be:
- What we really want is a more sophisticated method. (Preferred)
- A more sophisticated method is wanted by us.