Like fdb, I assume you mean this (from Oxford English Dictionary):
Originally Military. A bungled or botched undertaking; (also) a situation, state of affairs, or gathering (esp. a military operation) that is disorganized or chaotic.
Not this (ibid.):
A sexual orgy.
If, so, I'm highly doubtful that the Latin equivalent (at least the classical Latin equivalent) would be based on the same metaphor as the English. Instead, I tend to think that it would be something more scatological. Seneca the Younger, Apocolocyntosis 4.3 points toward a possible alternative:
ultima vox eius haec inter homines audita est, cum maiorem sonitum emisisset illa parte, qua facilius loquebatur: 'vae me, puto, concacavi me.' quod an fecerit, nescio; omnia certe concacavit.
Translation by P.T. Eden:
This was the last utterance of his to be heard in this world, after he had let out a louder sound from that part by which he found it easier to communicate: 'Oh dear, I think I've shit myself.' I rather suspect he did. He certainly shat up everything else.
The verb concacare (literally, 'To make foul with ordure, soil') doesn't have any derivatives, at least in classical Latin, but it's easy enough to use one of the standard suffixes that are added to verb roots to express the act or result of those verbs – for example, concacamentum (plural concacamenta) or concacimonium (plural concacimonia).
Furthermore, since a clusterfuck differs from a regular fuck-up in intensity and/or scale, you might add an adjective such as maximus ('the greatest, very great') or even merus ('nothing short of, pure, sheer, absolute, out-and-out'), and so render 'the clusterfucks' as maxima [or mera] concacamenta [or concacimonia]. (Note that no word for 'the' is needed in Latin.)
Alternatively, you could use a participle of the same verb, as in Petronius, Satyricon 66.7:
in summo habuimus caseum mollem ex sapa et cocleas singulas et cordae frusta et hepatia in catillis et ova pilleata et rapam et senape et catillum concacatum, pax Palamedes.
Translation by P.T. M. Heseltine and W.H.D. Rouse (revised by E.H. Warmington):
To finish up with we had cheese mellowed in new wine, and snails all round, and pieces of tripe, and liver in little dishes, and eggs in caps, and turnip, and mustard, and a mucked up dish – but hold hard, Palamedes.
This could yield something like res maxime concacatae, 'things very greatly shat up.'