Same thing here- I'm on 4.3 and there's no intuitive way to shut off the alarm My wife who's not a techie just gave up.
For example, the phone is on standby and the alarm goes off, I press the power button to get to the lock screen. Unlock the phone. But how do you turn off the alarm?
Down-swiping the left "notifications tab" gives the option to snooze or dismiss the alarm, but neither button does anything. You can't side-swipe the notification to remove it either because it doesn't go away.
What I've found that works is to bring up the Clock app where you can set the alarm (and incidentally, the alarm will display as being "off"). Then bring up the list of running apps (the Clock app should now be listed). Then press and hold the Clock app to bring up the menu to close the app. Closing the app should turn off the clock.
Go to the settings for the clock. The last thing on the list of things you can set is called 'Volume buttons'. Look at the options for 'Volume buttons'. Mine was originally set to 'Do nothing'. Change it to 'Dismiss'. You will then be able to turn off the alarm by pressing a volume button.
Did this, set alarm, it went off, but there was no volume icon on the resulting screen. However, I held down the flashing icon on the right, whatever it was, and it gave me a screen listing all the ringtones, as well as a cancel button. Humph. Not very user friendly.
Oh, you might have meant not an icon but the actual button on the top. It appears to be inaccessible due to my case. So I tried it again, this time without the case, and yes, the Dismiss setting allowed me to turn off the alarm with the volume button. However, for those with similar cases, if you hold down the right flashing icon, you will get a screen with the word Cancel, which also turns it off. : )