The biggest "sin" in this poem is dropping an apple, but the wider concept of sin, corruption, and the Fall of Man (from the Book of Genesis) seems to be hinted at strongly in the language and images. The speaker feels bad for the apples that have touched the ground and are consequently smushed up to make juice instead. This attitude suggests that he might feel bad for the human race as a whole, which often aims for lofty spiritual goals, only to get bruised – or worse – by earthly flaws. Frost seems to have absorbed the sin-haunted mentality of New England, present from the Puritans onward, but he also pushes back against it subtly.
Perhaps taking his cue from the Biblical line that "the wages of sin is death," the speaker fears his own death, in the form of a "long sleep" like the woodchuck's.
The poem demonstrates the power of tradition in the face of reason. Although the speaker does not believe that the fallen apples are worthless, he defers to custom in pitching them into the cider heap.