There are a lot of items in my app drawer, and I never use it to get to apps that are on my home screen. I'm wondering if there is a way to remove the apps that I have placed on my home screen from the app drawer to clear it up some.
Short answer, no. Your drawer is where all your apps are, in your homescreens you just have shortcuts to them and those can be deleted easily. But ...
With some launchers you can create folders or even tabs in the drawer. This way you could have one including the apps you access from the homescreen. Also, some custom launchers will let you hide apps in your drawer so you don't see them. But any way or the other all your apps will be on your drawer.
I have a OnePlus One. I use the "protected apps" section to hide some things I will never use, but if I put anything in there that I do use, it will disappear from the home screen as well, so that's not really a solution.
Creating a folder or hiding them using a different launcher isn't a bad idea. Would is slow down the performance of my phone? I am fairly new to Android, though I did have a GS4 when it came out and used a different launcher than the stock one from Samsung, but it gave me so many problems because they would both run at the same time.
Some custom launchers are heavier than others. My favourite is Nova, smooth and full of features. You won't notice any lag or battery drain.
In most launcher you'll have to pay for the full version to get some features like drawer folders or tabs. The best thing to do could be trying the free version first and then decide if you want to pay 3 or 4 dollars for the extra options. For me that's more than a fair price, but it's up to you. Worth a try, you won't regret it and you'll have fun in the process