You will need the Weed Whacker from the secret closet in the Captain's Quarters of the Hub, and you will attach it to the completed Mech (next to Sully's) to use it. The mech motor is in the production zone (far right) along with the key to the Living Quarters, which you need to get the Mech Crank (far upper left at the storeroom).
(see related question - this is most of the island)
It is at the far left past the living quarters. It is covered by vines that have to be removed.
you cant
You go to the bottom of the vines and click on the windows and they will kill the vines.
If you look down, you'll see three windows where the vines sprouted from. Go down and click on them to snap the vines and free him.
You just click the windows where the vines are coming out of. You click all three and the windows will close snapping the vines.
use the weed wacker. and press spacebar
When Sprocket is grabbed by the vines at the Captain's Quarters, slam the metal windows shut to cut the vines.
you can get it on the far left of steamworks island, past the living headquarters.
click on all three of the window to free the robot
Take it to the vine spot and click space bar to cut the vines. (it is to the left)
There are no windows that open inward on Steamworks Island. There is a skylight in the City Hall that can be opened with the Multi-Tool. You go out the hatch above Zack's room in the living quarters, to reach the Mech Crank on the vines.
It is by the "tightrope" vines at upper left past the Living Quarters. The only way to get there is through the quarters using the key, which is in a closet all the way across the island in the Research labs. (see related question)