With Slip-Stitch colorwork, you only use one of the two colors of yarn on any given row. Usually you work two rows of one color and then two rows of the other color. Since there are only two rows per color, the best thing to do is carry the unused color up the side. Ignore the other color while you are knitting. That's what makes Slip Stitch colorwork so easy.
And don't cut the yarn that you're not using.