If you mean to "make a game with the same game rules and logic, but with new code & new graphics", then yes, you can.
Copyright protects an expression of an idea, but not the idea itself. In the context of game development, an idea can be tic-tac-toe game. I write a webpage with JavaScript to play the game, that is my expression. You cannot reproduce my webpage without my consent, but you are free to code an exact replica of the game say, in iOS.
To prevent someone from making a game with the exact (or very similar) rules, you'd need a patent. Two famous games which are patented isare "Monopoly" (they got the name right!) and Tetris*. There is a reason why you see people making many Reversi, Sudoku, Tic-Tac-Toe etc implementations in the app store, but not Monopoly and Tetris.
*Technically, Tetris is not protected by patent, only by copyright. Many developers have rejected the company's copyright infringement claims as game design is not covered by copyright.