I assume you mean that you want to create a new list without a given element, instead of changing the original list. One way is to use a list comprehension:
m = ['a', 'b', 'c']
n = [x for x in m if x != 'a']
n is now a copy of m, but without the 'a' element.
Another way would of course be to copy the list first
m = ['a', 'b', 'c']
n = m[:]
n.remove('a')
If removing a value by index, it is even simpler
n = m[:index] + m[index+1:]