How to start the program from the beginning.

[deanhystad]

Your code is upside down. Instead of a function that asks if you want to play again you should have a function that plays the game.

import random

choices = "RPS"
win = {"R":"S", "P":"R", "S":"P"}
throws = {"R":"Rock", "P":"Paper", "S":"Scissor"}

def get_input(prompt, choices):
    """Get user input.  Repeat until valid input is entered."""
    while True:
        choice = input(prompt).upper()
        if choice in choices:
            return choice

def play_game():
    """Play Rock Paper Scissor against computer until there is a winner."""
    while True: 
        computer = random.choice(choices)
        player = get_input("\nChoose [R]ock, [P]aper or [S]cissor: ", choices)

        if player == computer:
            print(f"Computer throws {throws[computer]}. Draw!")
        elif win[player] == computer:
            print(f"Computer throws {throws[computer]}. You Win!")
            break
        else:
            print(f"Computer throws {throws[computer]}. You lose.")
            break

# Play until player wants to quit
while True:
    play_game()
    if get_input("\nDo you want to play again? [Y,N]", "YN") != "Y":
        break

Since user input figures so importantly in the game I wrote a function to simplify getting valid input.