What is the significance of the chapter in which Cash makes the coffin on a bevel?
We can say that the two concepts that anchor this novel are family and psychology. These concepts are intertwined in some complex ways and we can see this exemplified in the chapter that depicts Cash's thoughts on choosing to make his mother's coffin on the bevel.
In this chapter, Cash is shown to think in ways that demonstrate associative reasoning. One of the most notable elements of the novel is how it employs this type of reasoning and does so through stream-of-consciousness narration. In choosing to shape the style of the novel this way, Faulkner offers the reader a glimpse into the way that his characters' minds work.
In the case of Cash's decision to make the coffin on the bevel, we see what looks like a well organized, logical set of reasons for fitting the boards of the coffin together with a bevel. In thirteen numbered points, Cash thinks through the reasons for his decision, yet not all of the reasons are actually rational. They are logical, yes, but only logical in a very specific associative context.
The most telling and evocative line of this chapter is Cash's ninth consideration.
"The animal magnetism of a dead body makes the stress come slanting, so the seams and joints of the coffin are made on the bevel."
In his rather strange syllogism, Cash "proves" that in waking life people create a vertical stress and in sleep they create a horizontal stress, and so in death people must therefore create a slanted stress. This does not make rational sense, but it does follow a certain logic, just as Vardaman's thought follows a certain associative logic in the following chapter.
"My mother is a fish."
Each of the brothers is drawing connections in irrational ways, yet these irrational thoughts have a source in logic and reasoning. The stress of dealing with their mother's death has ostensibly rendered each incapable of thinking well or rationally. Thus, Faulkner's interest in psychology in the novel becomes an exploration how trauma functions in the mind and how it can lead to associative reasoning that goes unchecked.
In connecting Cash to Vardaman via associative reasoning, this chapter also shows that Cash and Vardaman can be contrasted to Darl and Jewel, each of whom think quite differently. Jewel is very much "in the world" and remains physical in his thoughts. Darl is the clearer thinker and does not engage in the kinds of associative reasoning that Cash and Vardaman do, although he does indulge in his intuition perhaps a bit excessively.
The chapter in question then carries a thematic importance because it exemplifies the novel's two central interests, demonstrating the effects of trauma on an individual's psychology and clarifying some of the familial position or roles that the various characters occupy.
Another point worth making here is that Cash's fixation on the work at hand may be intended to be understood as (1) a way for him to process his mother's death or (2) a way to avoid thinking about his mother's death.