Usually people get anxious and frenetic for new sources of income, to find new jobs, so they can maximize their patrimony as soon as possible, but many of them forget you don't accumulate wealth only when receiving money or being paid by others for a work. We can also decrease our expenses and stop third-partying tasks we can do ourselves, so at the end of a monthly cycle we will have earned more money to invest and make it grow overtime.
You are partly right, and besides, when you withdraw from spending, what you save is net, since it has already paid taxes. If you invest it or have it in an account that gives you interest, you will pay taxes on the interest or yield it gives you, but not on what you have already saved.
If you look for new sources of income, however, you will pay taxes on what you earn, although I prefer this option, without obsessing and stressing. Or even try to increase your current income without looking for new sources. With this you will be able to spend more and also save almost effortlessly.