Solution:
At the west of the island there is a crafting hut in disrepair. To rebuild it you must first drag a villager to the whale bones that are to the east of the crafting hut so they pick them up.
If you now take the bones back to the research area and drag another villager to the work bench they will craft a pickaxe tool which can be used to remove the roots of the tree. Afterwards builders can be put to work on rebuilding the craft hut.