To be beyond the bounds of imagination or belief, as in a surprising, shocking, or amazing occurrence. Well that beats all! I wasn't expecting to have you here for Christmas!
Surpass anything, especially in a strange or amazing way, as in Adam and his cousin Eve eloped-doesn't that beat all! This phrase appears to have replaced beat the Dutch. It is often used in a negative construction, as in the example. [Slang; first half of 1800s] Also see to beat the band.