For a list, you could use a list comp. For example, to make b a copy of a without the 3rd element:
a = range(10)[::-1] # [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
b = [x for i,x in enumerate(a) if i!=3] # [9, 8, 7, 5, 4, 3, 2, 1, 0]
This is very general, and can be used with all iterables, including numpy arrays. If you replace [] with (), b will be an iterator instead of a list.
Or you could do this in-place with pop:
a = range(10)[::-1] # a = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
a.pop(3) # a = [9, 8, 7, 5, 4, 3, 2, 1, 0]
In numpy you could do this with a boolean indexing:
a = np.arange(9, -1, -1) # a = array([9, 8, 7, 6, 5, 4, 3, 2, 1, 0])
b = a[np.arange(len(a))!=3] # b = array([9, 8, 7, 5, 4, 3, 2, 1, 0])
which will, in general, be much faster than the list comprehension listed above.