I have repaired crochet many times and cut in to a thread doily because I didn't want to rip out. I have repaired doily's and afghans that have had holes. When you look at attaching a new color of yarn to an existing strand of yarn, it is not much different.
The following is what I suggest for creating a new foundation, for a crochet afghan where the beginning is not as good as the rest of the project.
I suggest you carefully cut the loops on the previous row. Don't just cut through as you would a piece of paper or fabric because this will cut your next row as well.
I am including an image of single crochet with this example. You will see two vertical bars that the red arrow is pointing to in the first image. Right above it is a horizontal bar, which is the top of the single crochet for the same row. If you cut each vertical bar on the same row, your next row should remain intact.
In the second image, you can look above to the next row with the green arrow, and see the same vertical bars.
You will want to run a strand of yarn through the next row, just to keep all those stitches together and not pulling out of shape. Use a contrasting color so you can see the yarn. I have provided two images above showing how to run a strand of yarn between the stitches.
When you get the old section cut off, you will work a slip stitch or single crochet with your yarn color to secure that row. Make sure you knot well at the beginning and at the end. You are creating a new beginning foundation for your afghan, so you want to make sure you go through all your loops and everything is secure.
You can do this for shell stitch afghans with shaping. The bottom of each shell and stitch will need to be loosely secured together so they maintain their shape and the stitches do not come apart. If you worked the chain, you can slip stitch or single crochet a new chain to the bottom of the single crochet, chain 2 single crochet or slip stitch to the bottom of the 5 double crochet, chain 2.