When you make the mend, you just want to move the fly line that will cause drag. You don’t want to move the indicator and nymphing rig if you can help it. The easiest way to learn this to just pick up the line and set it down in a different spot.
When you need to make a mend, pull in most of the slack line and point your rod tip at the line you want to move. Now lift straight up and move the offending, drag inducing line to another spot. Viola!
This works because you are lifting the line straight up. The tension between the fly line and water is most easily overcome by lifting straight up. If you pull to the side, the water tension keeps the line on/in the surface of the water and you are more likely pull the line across/through the water instead of up. This will move everything connected to the line: leader, indicator, weight, flies. Additionally, your mend will not be sufficient and you will have to do it again.
After practicing the lift up and set down technique a few times, you will be able to do the mend and look like all of the other people who effortlessly throw a beautiful mend that doesn’t move the indicator. The first movement will be straight up to break the water tension.