Why does the poet use a mixed rhyme scheme in this poem?

Stevenson set this poem to a piece of music by Schubert, so it necessarily adheres to the regular rhythm of that musical tether. The rhyme scheme is one in which, by and large, every other line rhymes—so if we take the second stanza as an example, we see:
ABCBDBDB
Throughout all the stanzas, there is always this staple rhyming of the B lines. The variation comes in because some of the stanzas do throw in additional rhymes—so, for example, in the first stanza we actually see ABAB, and then BCBC in the second half of the poem. This is obviously a different rhyme scheme to the one in the first stanza, but the important thing is that it keeps to the same rhythm and retains the tether of the B lines. This is interesting because it suggests that the life of the vagabond is at the same time monotonous and changeable. There are elements in it which, like the vagabond's life on the road, go on "for ever"—this is the repeated B line, the rhymes on "me." However, the other elements represent the surprising and always changing things which happen to the vagabond as he proceeds on his unpredictable life. To an extent, he is tied to the life he has chosen, but in many other ways, he is freer than most of us to do what he pleases and deviate from the set path, as it were.

In writing "The Vagabond," Robert Louis Stevenson uses an irregular rhyme scheme to reflect the speaker's way of life. The speaker, as the title of the poem suggests, is a vagabond, a kind of tramp. He spends his days out in the open air, wandering from place to place, sleeping in bushes beneath the stars and catching fish in the river. The vagabond has no permanent place to call home; the whole world is his oyster. By most people's standards, this is an irregular life; there's no real structure to it. All the vagabond needs is an open road and the open air, and he's fine. He can go wherever he wants and do whatever he wants. Just as the vagabond rejects the conventions of society, so Stevenson departs from the conventions of poetry in adopting an irregular rhyme scheme.