It seems like the render that you are trying to cut out is on a background of one color like the sonic below.(It may be harder if the background of your render has lots of different colors.)
Correct me if I am wrong, but if the sonic posted above was your render, you only want the sonic.
There are actually TONS of different ways that you can cut out that render, but the easiest way to do it is by using the magic wand tool.
First off, what the magic wand tool does is select colors with similar RGB levels. This can be varied by the amount of tolerance. The higher percentage of tolerance, the more colors are selected, and vice versa.
Using the magic wand tool, select the portion of the image that you don't want. In my case, it would be the white background of sonic. Some colors in your render may have similar colors in the background so when you select the background, some parts of the render may also be selected. To fix this, just adjust the tolerance level of your magic wand. With the background completely selected, press the delete button on your keyboard. Now press Ctrl+A and copy your render into another canvas with your sig.
In this example, 50% tolerance was used to select the background. Notice how some of the closer RGB leveled colors were also selected.
With a tolerance of 29%, it is "Just right"