Is there another adjective for the mind other than mental which does not have negative connotations?

If I want to describe someone who has a great mind, or great mentality, describing him as a mental giant doesn't just seem right. Even though there isn't a comma between mental & giant, it may be misunderstood as calling someone mental & a giant.

Is there a better adjective which can be used here?

Alternatives for mental in the sense of relating to the brain and mental capabilities would include:

• an intellectual giant
• a cognitive giant (this is a bit weird)
• a cerebral giant

but you're probably better of going with the other suggestions and ditching giant for something that better matches what you're aiming at.

Seems to me the problem is the noun "giant." If you're emphasizing the mental capability, then make that concept the noun and modify accordingly. Some examples:

• Brilliant mind (simple phasing, often the best way to go)
• Gigantic brain (adhering to the original as much as possible)
• Deep intellect (similar to "towering intellect," a cliché, which can be understood as sarcastic)
• Cognitive wizard (emphasizes the magical)
• Perspicacious frontal lobe (ok, now I've gone too far)