Can I delete my Minecraft and download it again?

My Minecraft is laggy but my computer is new and has a really good processor, so that can't be the problem. Can I delete Minecraft and download it again without losing progress on singleplayer and without losing progress on some roleplaying servers I had?

Yes you can do that i have and it worked.

Hope this helped!

Servers are always saved on the server self so thats no problem, but to keep your singleplayer world you will need to put your worlds folder (-> %appdata% -> .minecraft -> worlds ) in a save place first then you can delete the whole.minecraft folder(don't delete you saved worlds folder and download it again. If you want to keep your server list you can save a server list ( its not a folder not really sure what it is )

Hope this helped.