You can assign them to never haul.

go into the labour menu and select the labour that you want to change (such as gathering plants). You can then change the option form 'everyone does this' to 'only selected do this'.
make sure to tick a few dwarves to actually do the task or else nobody will do it.

In the labour menu you can also click the little button on the dwarfs name (it looks like a green square with a hammer and a padlock on it). If you click it, it will turn red. This means that the dwarf will only do the labour tasks assigned to them.
You could (for example) tell your woodcutters to only do woodcutting, and nothing else. This will stop them doing other random tasks.

Another tip for getting the woodcutter to actually do the task is this: When designating trees to be cut down, click the little arrow at the bottom of the screen and that will give you an option to change the priority of the job. If you set it to 1, the tree cutting will be highest priority and they will cut the tree before doing any other tasks (hopefully).

Also, be careful putting woodcutters in the military. Ive found it can mess up their equipment pickups somehow. If they have an axe assigned to them in the military, they wont use the same axe to chop down trees or something. Im not sure exactly how that works, Ive just found having them in the military caused problems for me.