I'm not sure if you're literally throwing away ideas, as in throwing the paper in the trash, but whatever the case I advise you to keep everything. I never throw away my ideas that I put on paper, no matter how bad they seem to be at the time, and no matter how alike they are to another game. Why? Because I threw down all of that stuff on paper because
I wanted to.
I was inspired to make it. It came from me; it came from what I enjoyed. And I've found that those notes and doodles can spark something in me years later if I look at them again, and what may have once been a crappy or tiny idea suddenly becomes inspiration for something super good and fun. You can even get some motivational nostalgia from old ideas and drawings.
I have 9 notebooks completely full of different game ideas and designs from over the years, and then I have a LOT more stuff in Microsoft OneNote as well. Even if I threw down some crappy fan game ideas years ago, it's amazing how I can look at some of those now and think, "what if I replaced the Nintendo characters with my own?", or "what if I used this part of the story in another game, scrapping all the stuff about Princess Zelda and the Goomba Unicorn Candies?"
As a result of me going over old papers and notes filled with game-related ideas and doodles, I've easily been able to get myself out of an uninspired rut multiple times. I've been able to get an idea on a script I want to create which lets me increase my skill and efficiency with GML. Sometimes I've been inspired to try a new prototype of some super weird thing... uh, but those have almost always turned out horrible... but that's beside the point, I guess.
But anyway, lastly, there is a game I've been making for a while now and my old papers have played a key role in shaping the key points of the game, bringing in new mechanics and whatnot. So I'm basically just saying that
you would be surprised how helpful "crappy" ideas and designs can be to give birth to awesome stuff.