Oh! That's because your code only works for such word!
You should've stored the slice of the string stored in new_word into another or same variable.
new_word = new_word[1:len(new_word)]
Doing new_word = "ordway" is actually not correct.
1) word: contains your original string, the one it was informed by the user.
2) first: contains the first letter, , of the original word that was informed by the user.
3) pyg: contains the "ay".
So adding them would lead into something like this:
word contains "c"
first contains "cake"
pyg contains "ay"
Concatenating them into new_word will result into: "ccakeay"
Alter the order to : first + word + pyg so it will turn into "cakecay"
If you do new_word = new_word[1:len(new_word)] it will go from position  to the last position so it will get the correct value which is "akecay".
Edit: No problem! Quote me if there's something else I can help you with