[Hmmm... that's strange. I responded to this a couple of hours ago, but it still hasn't shown up. My apologies if this is a duplicate response.]
Go to the main foreign relations screen, where you see the major races listed in medium-sized boxes in the middle-upper-right of the screen. There will be one race listed in a larger box on the left (the one you've selected or the default if you haven't selected one yet). Click on the race who's your ally, and that race will become the one in the large box at the left. Under the portrait is a small box "Break Alliance". Click on that and the alliance is immediately broken.
It might be too easy to do (there's no confirmation required), and I'm surprised I have never accidentally broken an alliance yet.
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