Yes, you can use a regular expression for this:

import re
output = re.sub(r'\d+', '', '123hello 456world')
print output  # 'hello world'

Try something like below:

import string
import re
import nltk
from nltk.tokenize import TweetTokenizer

tweet = "first think another Disney movie, might good, it's kids movie. watch it, can't help enjoy it. ages love movie. first saw movie 10 8 years later still love it! Danny Glover superb could play"

def clean_text(text):
    # remove numbers
    text_nonum = re.sub(r'\d+', '', text)
    # remove punctuations and convert characters to lower case
    text_nopunct = "".join([char.lower() for char in text_nonum if char not in string.punctuation]) 
    # substitute multiple whitespace with single whitespace
    # Also, removes leading and trailing whitespaces
    text_no_doublespace = re.sub('\s+', ' ', text_nopunct).strip()
    return text_no_doublespace

cleaned_tweet = clean_text(tweet)
tt = TweetTokenizer()
print(tt.tokenize(cleaned_tweet))

output:

['first', 'think', 'another', 'disney', 'movie', 'might', 'good', 'its', 'kids', 'movie', 'watch', 'it', 'cant', 'help', 'enjoy', 'it', 'ages', 'love', 'movie', 'first', 'saw', 'movie', 'years', 'later', 'still', 'love', 'it', 'danny', 'glover', 'superb', 'could', 'play']

Would this work for your situation?

>>> s = '12abcd405'
>>> result = ''.join([i for i in s if not i.isdigit()])
>>> result
'abcd'

This makes use of a list comprehension, and what is happening here is similar to this structure:

no_digits = []
# Iterate through the string, adding non-numbers to the no_digits list
for i in s:
    if not i.isdigit():
        no_digits.append(i)

# Now join all elements of the list with '', 
# which puts all of the characters together.
result = ''.join(no_digits)

As @AshwiniChaudhary and @KirkStrauser point out, you actually do not need to use the brackets in the one-liner, making the piece inside the parentheses a generator expression (more efficient than a list comprehension). Even if this doesn't fit the requirements for your assignment, it is something you should read about eventually :) :

>>> s = '12abcd405'
>>> result = ''.join(i for i in s if not i.isdigit())
>>> result
'abcd'

Change

for word in word_list:
    word = punctuation.sub("", word)

to

word_list = [punctuation.sub("", word) for word in word_list]    

Assignment to word in the for-loop above, simply changes the value referenced by this temporary variable. It does not alter word_list.

You shouldn't iterate & try to change the object while iterating. This is complicated by the fact that strings are immutable (new reference is created when string content changes). Well, not a good solution, and not performant either even if you could make that work.

A pythonic & simple way of doing this would be:

new_string = "".join([x for x in string if not x.isdigit()])

(list comprehension which creates a new string keeping all the characters but the numerical ones)

could be "translated" for the non-listcomp speakers as:

l = []
for x in string:
    if not x.isdigit():
       l.append(x)
new_string = "".join(l)