as we express our gratitude是as引导的时间状语从句,作整个句子的状语.
we是主句主语,must never forget是主句谓语,that the highest appreciation is not to utter words,but to live by them整句话是must never forget的宾语从句.
在that the highest appreciation is not to utter words,but to live by them这个宾语从句中,用了not...but...这个结构,意为“不是……而是……”.
如果还不清楚,可以继续追问.：）