As explained in Timothy White's CATCH A FIRE book:      
                                                                              
In what seems like a simple allegory in which a woodsman informs a large tree that it is about to be felled, "Small Axe" is actually a fascinating three pronged assertion that is readily understood by all Jamaicans but utterly obscure to almost anyone else.

Not only is "Small Axe" intended as a warning to oppressors everywhere that the people of the Third World will one day cut them down to size, but it is also a bit of bravado that had a particular application to the Jamaican recording industry. When the song was originally written by Marley and noted Kingston producer Lee Perry, it referred to "the Big T'ree," the island's dictatorial record company triumvirate-Dynamic, Federal and Studio One.

And the central image of tree-felling, accompanied by the excuse that it is being done according to the wishes of a superior, is a sober throwback to the old plantation-era pecking order, when slaves who were ordered to topple the island's gigantic silk-cotton trees, which they held sacred, would sprinkle some rum on the roots of the trunks and sing a woeful song. This was done to assure the spirits lurking within that this destruction was not the slaves' idea, but rather the will of their masters.