Yes, solving puzzles will help you sharpen your mind, depending on the nature of the puzzle. Also, puzzles don’t even need to be done on a daily basis but it helps your brain more if you can find the time to do some sort of puzzle every day. By puzzles, I don’t just mean jigsaw puzzles. Really, most any puzzle/game works to sharpen your mind by stimulating your brain and by helping it to make new connections.
That is why it is important to choose challenging puzzles. It’s also important to choose different puzzles. If your brain is used to playing, for example, Spider solitaire, try making it more challenging by playing a two-suit version instead on just one suit.