There are many answers already that tell you how to make a proper copy, but none of them say why your original 'copy' failed.
Python doesn't store values in variables; it binds names to objects. Your original assignment took the object referred to by my_list and bound it to new_list as well. No matter which name you use there is still only one list, so changes made when referring to it as my_list will persist when referring to it as new_list. Each of the other answers to this question give you different ways of creating a new object to bind to new_list.
Each element of a list acts like a name, in that each element binds non-exclusively to an object. A shallow copy creates a new list whose elements bind to the same objects as before.
new_list = list(my_list) # or my_list[:], but I prefer this syntax# is simply a shorter way of:new_list = [element for element in my_list]To take your list copy one step further, copy each object that your list refers to, and bind those element copies to a new list.
import copy # each element must have __copy__ defined for this...new_list = [copy.copy(element) for element in my_list]This is not yet a deep copy, because each element of a list may refer to other objects, just like the list is bound to its elements. To recursively copy every element in the list, and then each other object referred to by each element, and so on: perform a deep copy.
import copy# each element must have __deepcopy__ defined for this...new_list = copy.deepcopy(my_list)See the documentation for more information about corner cases in copying.