He had another motto, which was emblazoned across the crest of the front page of his newspaper, The Liberator: "That which is not just is not law". At the time he started publishing he meant to suggest that it was a moral imperative that Christians and Americans should disobey unjust laws, such as the Fugitive Slave Act, which required that northerners report and turn in runaway slaves whenever they saw them, essentially deputizing the entire North. Garrsion felt there was no democratic or Christian way in which he could or should be required to do so, and advocated breaking that law, among others.
This can be found in the book's preface, which was written by William Lloyd Garrison. At the very end of his preface, he gives his motto. It is
-"NO COMPROMISE WITH SLAVERY! NO UNION WITH SLAVEHOLDERS!"
What this means is that Garrison is a very radical abolitionist. He is much more radical, for example, than Abraham Lincoln ever was (and this was written before anyone had ever heard of Lincoln).
What he is saying is that Northerners should never accept being in the same country as slaveholders. He is saying that they should not compromise to stay together. What this means is he thinks they should ban slavery immediately.