Yes, a synonym for "beyond exhausted" could be "utterly fatigued" or "completely drained." Other phrases like "totally wiped out" or "bone-tired" also convey a similar level of extreme fatigue.
dyspnea
Exhausted
Exhausted. Tired. Worn out. Worn. Weary.
fatigued,exhausted,sleepy ---------------------------------- bushed, shattered, worn out , beat
immeasurable
Freezing
over, beyond, opposite, cross
They were exhausted.
Stunning, bewitching, unexpected, beyond expectations
in the sentence "joe is exhausted" exhausted is a pronoun, describes "joe" the noun in the sentence "joe exhausted all of his options" exhausted is a verb, describing what the noun is doing or has done depends on how the word is being used
exhausted
Haggard is an adjective meaning to look unwell or unkempt. The closest synonym to the word would be exhausted or drained.