After building the mech (get the motor and crank), climb aboard the Mech and select Equip on the Weed Whacker on your items. To use the Weed Whacker to "splat" plants, aim up or down with your mouse and press the spacebar.
to work the weed wrecker where it and press space
The Weed Whacker attachment is in the quarters of Captain Ziggs, on top of the Hub. You have to complete the Mech in the garage next to Sully's, then attach the Whacker to it. This will let you enter the door at the far left of the island, using the spacebar to activate the Whacker.
pound it with the mech's weed whacker
Once you have attached the Mech Crank and the motor, enable the Mech Weed Whacker and use the spacebar to whack the weeds (you need at least two hits per section on weed growth).
The Mech Walker is the key to entering the storeroom and defeating the monster plants that are active there. Once you finish the Mech with the Motor and Crank, you can attach the Weed Whacker attachment and enter the door at the far left of the island.
You cut the weeds blocking the door of the Storeroom far left of the island) with the Weed Whacker. The weed whacker is in Captain Ziggs' room atop the Hub, and must be attached to the Mech Walker (in the garage next to Sully's). Finishing the Mech requires the Mech Motor and Mech Crank.
Find the weed wacker and attach it to the robot body, which you also have to find and activate.
weed whacker
weed whacker
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)
One is in the crab, one is in the captians quarters secret room (also get the weed whacker) and the last one is in the botannical library (across the bridge). the alarm will go off on that one but it doesn't matter.
Clearing the weeds from the entrance at far left (the Storeroom) will have to wait until you finish building the Mech walker, which is in the garage next to Sully's. The weed whacker attachment for the Mech is in Captain Zigg's quarters on top of the Hub. When the Mech is finished, climb aboard and use the weed whacker card. Aim with your cursor and press the spacebar to whack weeds.