Is it possible to save my project out of arduino?

I have just get my project done but i need to start a new one, i was wondering if i could replace my atmega and connect this to my circuit?, so i dont need to get another arduino which would be just waste money

Yes. You can move it to a breadboard arduino.

I use Arduino Nano devices for projects. They cost $2-3 each on eBay (oftern less than buying the ATMega chips on their own) and I don't mind leaving them with the project.

I don't get it. Every time you save your code in the Arduino IDE, you have preserved it. You can now go do whatever you want with that same board, and reload your saved code later on.