I think I recall another definition:
In politics, when a presidential nominee has chosen but not announced his running mate, he wants a thorough check to be sure the mate's past has no hidden "embarrassing incidents" that might be revealed during the campaign. The searching scathing background-check is called "taking him behind the woodshed", or "woodshedding".

For example, as I recall: in 1968, after Senator Eagleton was announced, it was discovered that he had been treated for a nervous breakdown. The comment was that the Democrats given their candidate a proper woodshedding.