First I would make sure your mod file is named "Mods" and make sure when you click on the game icon it actually launches smapi command console. Launching the game through your files: If you go into your game's files there is StardewModdingAPI (SMAPI) application which launches modded SDV. The plain "Stardew Valley" is how you launch the game without mods. Launching the game through Steam: Make sure the file pathway is linked to the SMAPI version in your game file.
I do realize that your issue is making a save so I recommend making sure there is nothing wrong with your save files, it is possible that in creating the mods folder something messed up your other files. I recommend uninstalling smapi and reinstalling. Afterwards you should have 4 folders in your game file "Content", "Mods", "save-backups", and "smapi-internal" followed by all the different extensions the game uses. If you have any other details I may be able to help further.