How do I say that something is "negative"?
According to iCIBA:

If someone is a negative person, or has a negative attitude, then they are 消极 (xiāo jí), or  悲观 (bēi guān).

To say that a word has a negative connotation, you use 负面含义 (fùmiàn hányì), literally, "downside meaning".

Thanks to S.Rhee for pointing me to iCIBA, where I was able to find the answer to my own question.