Saving money = not spending it 
Not spending it? Maybe it would be better to say do not spend your money in not so important thing. Just spend it in important matter/things. Coz no one is not spending their money. Wether you like it or not you will spend your money.Saving is not to spend it. The savings will be spent later. It is better to increase the spending power in the saving process by investing wisely.
Well that's is clear to everyone, without money you can't save anything, the original topic was assuming that you had money in the first place, to proceed to save a small portion of it is better to invest them.
You need to calculate the risk and reward for this, if the risk is lower you have found your good investment and you can invest without worry too much, if you end up losing anyway, you will go to another investment with less risk and so on, in the end, seeing that the chances are with you, you will earn money on top of your saving. I think that you need to move you saving to save even more money, leaving them sit under your pillow isn't a good idea.