Explain how Uncle Tom in Uncle Tom's Cabin suffered from slavery.
I have changed your question because it did not make sense to ask how the book itself suffered from slavery. Therefore I assume that you are asking how the character himself suffered.
Uncle Tom suffers from slavery in ways that are both physical and emotional/spiritual. His suffering, of course, comes to a climax when he is killed because of his status as a slave.
Before Uncle Tom dies, he suffers emotional losses. Because of the slave system, he is sold away from his wife and children. Because of the slave system, he is told that he will be freed but then loses out on that prospect when the master who made that promise is killed before he can carry it out -- this shows how totally Tom is in the control of others.
The final part of Tom's life shows him suffering physically because of slavery. Simon Legree and the overseers beat him, eventually killing him, because Tom will not do the things that are required of him in this system. These are unreasonable demands (beat your fellow man, stop trying to comfort them with the Bible, etc) but they are part of the slave system.
In these ways, Tom is abused both physically and emotionally by the slave system.