Basil from Cuttings

Can you start new basil plants from clippings?

Yes, but they won't reach usable size as quickly as seed grown plants. We use the method at times when we are out of a particular kind of seed. Also if you make a large number of cutting grown plants, they will be more susceptible to diseases racing through the whole group, because they are genetically identical.
To make the cuttings be sure to use sterile sand or pasteurized soil as the rooting medium and keep the humidity high around the cuttings to prevent excessive wilting of the one or two leaves you leave per cutting. Make sure you cut the stem just below a node(the thickened portion of the stem from which the leaves emerge) and make sure you plunge the stem deeply enough into the soil so that one or two nodes are inserted into the soil. The first roots will come mostly from the nodes.