If I turn off icloud Photos upload, when I turn it back on will it upload all my new photos?

As you mentioned .

I have an iMac and have been noticing some processes associated with Photos have high CPU usage which apparently is slowing down other programs.

See the article Quit an app or process in Activity Monitor on Mac - Apple Support

View CPU activity in Activity Monitor on Mac - Apple Support

Read Set up and use iCloud Photos - Apple Support

How iCloud Photos works

iCloud Photos automatically keeps every photo and video you take in iCloud, so you can access your library from any device, anytime you want. Any changes you make to your collection on one device change on your other devices too. Your photos and videos are organized into Years, Months, Days, and All Photos. And all of your Memories and People are updated everywhere. That way you can quickly find the moment, family member, or friend you're looking for.

Depending on your internet speed, the time it takes for you to see your photos and videos on all of your devices and iCloud.com might vary.

Click on finder > Go > hold option key > click on library , if you create folder in first column and photos are saved in that folder , or you have saved photos in iCloud Drive ( archive ) , pictures , drop box folder they will occupy hard drive space .

See a thread Cloud and Hard Drive - Apple Community

Photos are synced with iCloud , once you delete photos from iCloud.com , they are deleted from Mac photo application , if you export massive photos to some location Export photos, videos, slideshows and memories from Photos on Mac - Apple Support the Macintosh HD space will be exceeded / occupied as if you compare 116GB iCloud photos with 250 GB hard drive space .

Note : you don't want to loose photos from iCloud , purchase new iCloud storage plan Upgrade to iCloud+ - Apple Support

"iCloud Photos automatically keeps every photo and video you take in iCloud, so you can access your library from any device, anytime you want."

I have a brand new computer. I have signed into my accounts on this computer and now there are 116GB of photos on my computer that only has a 250GB HD. I don't want my images stored on this device. What do I need to do to get these files off of my computer, but not lose them from my cloud?

But that is the thing, I didnt export massive photos to some location. I turned on my computer, started singing into my apple accounts, and now there is 116 GB of photos on my HD space. I didn't export. I didn't ask to store my photos on my computer. I turned on my computer for the first time, signed into my apple accounts, installed some apps that I would be working on. Nothing else. But my computer is saying that I now have 116GB of Photos taking up space on my unused computer. I don't want half of my hard drive space that I can use not taken up by photos I didn't ask to store on my computer. How do I have this not happen?

Firstly, thank you for continuing this conversation and trying to help. So I have a laptop, an iMac and now this new MacMini. Are you saying that all of my computers have 166GB of space being taken up on them because my iCloud is signed in on each computer and all my photos/videos etc are saved to the cloud?

When three computers are signed in with same Apple ID and password on the same network , every default settings like iCloud Drive , desktops and documents box , all default applications notes , photos , calendars .... are checked the iCloud data will be similar , when complete syncing is saturated .