A Sieve of Eratosthenes
Agreed, this is not the Sieve of Eratosthenes. This is trial division by primes. (As long as you're doing trial division, you can do it slightly better, and only test up to the square root of the number.)
Replace the while loop, making it clearer and more pythonic: for test in num_list:
It is inefficient to delete from the middle of a list in python, which takes O(n) time.
It is generally unsafe, and will give wrong results to delete from an collection WHILE iterating through it. In this case it seems to work, but be careful. I would instead keep a binary flag for each number, with whether we've found a factor already or not (array of True/False).