The irony here is that the accident happens at the end of the work day, at a time when the boy might have been dismissed to take an extra half hour to himself. In fact, his sister is even there saying that supper is ready. Because he is not allowed to leave, however, he is still working later, when he is injured. It may even be the fatigue of a long day that led to the accident. If the boy had only been able to go play, he would still be alive, with an intact hand. Such is the irony of the poem, with the speaker's rueful wish that they might have told him to "call it a day." The speaker sympathizes with his character, portraying the events of the poem as out of the boy's control.

How is the time of day ironic in "Out, Out—" by Robert Frost?

The time of day is ironic because it is dinner time and the end of work, but also the end of the boy’s life.

Irony refers to something unexpected happening.  It means that there is a double meaning or an unusual occurrence.

At the beginning of the poem, Frost establishes the time of day right away.

And from there those that lifted eyes could count

Five mountain ranges one behind the other

Under the sunset far into Vermont.

Sunset, and supper, are symbolic of something ending.  As the day is coming to a close, the boy’s life is coming to a close.

The speaker comments that he wishes they might have let the boy come in just a little early, because it would have changed everything.  If the boy had come in before his sister distracted him by calling that it was suppertime, and causing him to lose his hand—leading to his death.