To take (someone) to the cleaners has three meanings. The Concise New Partridge Dictionary of Slang and Unconventional English defines them:
cleaners *noun*: take someone to the cleaners, 1 to thrash someone, UK 1976. 2 to thoroughly swindle or rob someone, US 1907. 3 to forcibly strip someone, UK 1997
The American Heritage Dictionary of Idioms defines the first two meanings as slang; early 1900s and you can find German equivalents here. There's another variation, put the cleaners through (someone).
Here's some earlier antedatings to Callithumpian's 1929, all three published in the USA.
A letter from W. H. Emrick printed in the April 1914 Electrical Worker (Vol. XIII, No. 12, page 182, pdf):

At present we are not in a position to say what the outcome will be but have high hopes of taking the Employers' Association to the cleaners.
The 1921 Lady Luck by Hugh Wiley (Project Gutenberg: plain text):

Starting in the sunshine of Lady Luck's smile, the Wildcat cleared the hurdles of financial ruin and rambled into the stretch soggy with a cloudburst of hard luck. He staked his last pair of ten dollar bills on a throw whose momentum carried him to the cleaners.
The 1922 Riders Up! by Gerald Beaumont (archive.org: read online, or plain text), page 175:

"Oh, Susanna !" he cried. "I got you!" I win
the pup with the screw tail! Twenty minutes for
a new book, gents; and — believe me or no —
Susanna and I are going to take you all to the
cleaners!"
This book is about horse racing and gambling (a lot of gambling) and contains many similar references to cleaning for taking money. Cleaned up:
"The old firm's grown a bit, Billy. I had contracts for ten bottoms at sixty-eight dollars a ton
when the war broke out. Cleaned up a million
and a half on each contract almost overnight.
Sold five ships and put seven and a half millions
into the South American end of the business.
Caught the market right on sugar — another five
millions. Now we've got three millions in Liberties, ten ships worth one hundred and eighty
dollars a ton, a warehouse valued at two million,
and we're cutting into the British trade from one
end of the south coast to the other. Billy, my
boy, you've been through hell, now I want you
to have your share of fun. Forty millions in
assets, and I rolled it up all for you. Help yourself, boy — hit 'em hard and high, the old man
loves you!"
Clean sweep:
He was
rather hopeful of a clean sweep in the gaited
saddle class, but the moment the spot-light disclosed the final challenger, Van Buren drew a
quick breath and acknowledged himself beaten.
Clean-up:
Between them, they made
pretty much of a clean-up in the National Coursing Stakes and the North American Field Trials.
And finally, this is a nice one:
The
truth was that there were many visitors in Dominion Springs who were exactly in the Kid's
predicament, for the town boasted seventeen
bathing-places, one hundred and fifty games of
chance, and a race track. For its size it was undoubtedly the greatest cleaning establishment on
the continent.