I found two similar patterns on Ravelry.
Sounds like they're knit from the bottom up, all the pieces are held on stitch holders and then joined on one needle for the yoke knitting with raglan sleeves. If so, I would only leave the yarn attached to the piece that you knit first once all the pieces are joined for the yoke. That'll be the right front starting at the neck edge on the RS row or the left front neck edge if you're starting on the WS row.
For the back you can certainly cut the yarn leaving about a 4-6 inch tail to weave in later.