Does this solution look....Pythonic? :)

Yes. I would call it "Pythonic". There are always other approaches, but following a natural flow as you see it is often much more readable and understandable than some overly "clever" solution. As for the posted code, I would consider the following changes:

def disemvowel(word):
    letter_list = list(word)
    vowel_list = "aeiouAEIOU" # This can stay a string.
    for letter in vowel_list:  # "in" works equally as well on strings and lists
        while letter in letter_list:  # parens not needed and can be distracting
            # since the following command will not execute unless the letter is present
            # the try is not needed.
            letter_list.remove(letter)
    new_word = ''.join(letter_list)  # Not good practice to overwrite the argument
                                                       # variable as it could affect code outside of the function
    return new_word

Beyond being Pythonic, performance is important. Think about how many times the word list is scanned. The while scans the letter_list looking for the current letter. If one is found, remove() is called. This also scans the list looking for the letter to remove. So for each vowel that exists, in the original word, the letter_list is scanned twice. As the removing proceeds, all the scans must travel farther and farther down the word to find a match and a removal. This is repeating comparisons that have already been make. (the first not vowel would be compared again on every pass through the loop. It might be better to simply accumulate the "keepers" so it's done in one pass:

def disemvowel(word):
    """10*n comparisons for words of length n"""
    result = []
    vowel_list = "aeiouAEIOU"
    for letter in word:
        if letter not in vowel_list:
            result.append(letter)
    return ''.join(result)

Post back if you have more questions! Keep at it!!