Drawing spirals on virtual whiteboards
The standard way to do this would be to use a tkinter canvas or pygame, but rolling with your method, you only have one huge efficiency problem, you are wasting subpixel precision on your calculations, I added a simple PRECISION constant so that you can decide at will how many degrees you advance per step, you only used 1 degree per step that is really to little, I suggest \$10\$, it looks good and goes fast.

I  also added a constant for 10**5 so that you can avoid computing it every cycle (not a big deal) but mainly so that you could explain with a name what that number does.

I also replaced the while loop with a for loop so that the program does not run indefinitely (I was quite trolled by the program taking my mouse cursor for infinite time, it was not easy to shut it down).

Also please put care in your comments, about spelling formatting etc.. and the standard format is a docstring on top of the file.

Removing the printing can also speed up your program a bit.

Enjoy your improved program:

"""
This program takes control of the mouse to draw an ellipse.

(x-h)^2 + (y-k)^2 = r^2
Knowing radius and degree,
rise = r*sin(deg*pi/180) 
run  = r*cos(deg*pi/180)
"""

from numpy import sin, cos, pi
import pyautogui as cc
import time

BIG_NUM = 10**5
PRECISION = 10 # higher is less precision
ITERATIONS = 300

input('Enter to Begin\n--&gt;')
radius = int(input('What do you want your beginning radius to be?\n--&gt;'))
rate = int(input('How much do you want it to increase by each cycle?\n--&gt;'))
h, k = cc.position()
degree = 0
x = h+radius*(int(cos(degree*pi/180)*BIG_NUM)/BIG_NUM)
y = k+radius*(int(sin(degree*pi/180)*BIG_NUM)/BIG_NUM)
cc.moveTo(x, y)
cc.mouseDown()

for i in range(ITERATIONS):
    degree += PRECISION
    degree %= 360
    radius += (PRECISION * rate) / 360
    x = h+radius*(int(cos(degree*pi/180)*BIG_NUM)/BIG_NUM)
    y = k+radius*(int(sin(degree*pi/180)*BIG_NUM)/BIG_NUM)
    cc.moveTo(x, y)
    #print('Cords: '+str(x)+'||'+str(y))
    #print('radius: '+str(radius))
    #print('degree: '+str(degree))
    #print()