Well, after you have tried all your options and found the snapper to be unimpressed (usually due to the fact that they have so few natural enemies that they can't eat or severely maim, and thus do not feel any urgency to relocate if it has found your yard to its liking), you use the, um, tastiest method...
Just don't get emotionally attached as it will make converting the critter into a comestible rather difficult. (You can still do this without shooting it, but it will not live through the conversion process so choose a humane mode of dispatch - consult your friendly Religion of Peace practitioner for techniques to use for following the method espoused in the recipe.)
Now, if converting the critter into a kettle of tasty soup is beyond your comfort level, depending on the size of the critter you can just pick it up carefully by the edges of the shell (watch that neck - it has a longer range than you think and it has a vise on the end that you don't want your fingers in - and deposit it in a suitable container for transport to someone else's property, preferably near a waterway that is not connected to whatever is close to you. Caution: this only works with relatively small specimens.
Critters with some size (and weight) are a bit more difficult to handle in this manner because the increased size and weight also increases the squirm factor and the effective range of the front mounted power vise. Did I mention that once they bite onto something, finding the magic release lever is not as obvious as on a visegrip pliers - because there is no magic lever to click. And whatever is locked in the critters jaw will stay there. Until the critter no longer feels attacked. Or until you chop off its head to retrieve your fingers. (If you get to this point, might as well follow the recipe above.)
Herein lies a method of attending to the larger critters if you really decide that you don't want that kettle of soup.. Find a tree branch, stick, piece of wood of a size suitably appropriate to the size of the soup ingredient, er, snapper, that you are about to play with. Offer the stick/similar device to the turtle is such a manner that the critter will strike at it. The desired effect is that said soup pot escapee will grab hold of the stick. As long as you keep tension on the stick, the turtle will continue to hold the stick in its mobile vise. (You need to convince the turtle that the stick is continuously attacking him/her to maintain turtle's interest in the stick instead of it thinking your fingers look kind of like - food... or an enemy...)
Now, depending on the size, you can lift the turtle via the stick stuck in its vise device, or enlist a second person to pick up the critter by the edge of the shell (being sure to produce tension on the stick stuck in the vise devise so that the vise does not unattach from the stick and reattach to the fingers that are lifting the owner of that vise devise - have I mentioned this point enough?) and deposit into a tub/bucket/wheelbarrow/enclosure of your choice for transport to your neighbors back forty. If critter is enclosed in a manner that will provide isolation of your tender parts from turtle visegrip jaws, you may release tension on the stick and turtle will eventually decide that sticks are not on its diet today and were probably not a threat either and release the stick (Keep this point in mind for the next step..)
If the business end of the turtle is sufficiently isolated from your tender parts when you arrive at its destination, you may carry the bucket/tub/whatever to a proper location and just unceremoniously dump the beast out (gently of course so as not to bruise the turtle meat, someone might want that kettle of soup you released.) If the mobile visegrip is not sufficiently isolated, offer it the stick once more to keep it occupied as you follow the step immediately above.
After you have blessed your neighbor with the fixin's for a great kettle of soup, give them the recipe before you drive, sans soup, back to your abode, now rendered turtleless and soupless, or at least turtlesoupless...
After you have released your snapper soup fixins so that your neighbor can enjoy the soup you missed, you can still fix your self some snapper soup but the turtlemeat will cost you more than the free one provided that you spurned... See HERE...
Thank you! This all sounds more complex and difficult than I originally thought. I’m going to have to enlist some help. Isn’t there a television about some guys who capture alligators? I wonder if they’d want to go after a snapping turtle.