How to Propagate/Root Salvia Cuttings:
First I locate an ideal stem for cutting. This particular stem has three nodes - one apical bud (at the stem tip), and two other nodes. I've done stem tip cuttings of salvia with only two nodes before so it will work but three will result in a larger plant a little bit faster. Once I've targeted the salvia stem tip I want I cut just below the bottom node. The nodes contain auxins which are naturally occurring growth hormones used to induce root or leaf growth.
Here's a look at the salvia cutting after I've separated it from the plant. Notice that there are several leaves that aren't necessary. I remove all the leaves except for two and pinch off the apical bud. That will encourage the auxins to work toward roots rather than making new foliage at the top. Once the salvia has rooted it will also encourage lateral branching for a nice bushy plant.
Here's how the cutting looks after leaf removal. Two leaves and two nodes with a little bit of stem in between.
The next step is to dip the cut end of the salvia cutting in rooting hormone then stick it in moist rooting medium. Then I'll wait for 10-14 days until rooting has occurred. Once I have roots I'll pot up my new salvia. It should bloom by the end of this summer (at least here in Tennessee other zones may have different results). I've had success using this method with many other plants - go ahead and give it a try!
It doesn't hurt the plant and makes it encourages it to become more full of foliage. Hopefully you can see why I want to make more salvia!