In the original game, you were able to delete character files whenever you wanted and you could get two different endings depending on if you deleted Monika's and/or Sayori's Character file. I wanted to try this again with the new game but I couldn't figure out how. Any help would be greatly appreaciated!

It is locked until you clear the game once. Afterwards, you can delete Monika before starting a new game. Deleting Sayori is no longer an option.

If you delete Monika before starting a new game Sayori will freak out and abruptly end the game. Restart the game at this point and Sayori will already have hanged herself. Let her dangle for 10 minutes (..) and get a message.
This was also a feature in the original game, though

where do you delete her??

Originally posted by DarkestPrayer69:

where do you delete her??

In the menu. Monika flat out tells you how..

Also, you're required to delete Monika in Act 3 in order to proceed to Act 4..
Whether you've done the other requirements determines if you get the good or bad ending. Act 3 isn't an ending, it just goes on forever until you delete Monika..

Deleting Sayori is just a neat easter egg and nothing more.