Tp 'tick off' started life as the military term, 'to tell off' which also now means 'to scold'. Originally, it meant to sound off numbers in order, as a rank of soldiers might shout out one after the other: "One! Two! Three!" and so on. In typical military style, this was a bit like 'ticking things off' - ie indicating they were all present and correct - on a list.
In the scolding context, it suggests the person doing the scolding is listing the poor culprit's faults one after the other, ticking them off on paper as he goes.