After he returned from his 1928–1929 Paris sojourn, Davis painted several scenes in which Parisian and American imagery was placed against an undefined background. In Still Life with Saw, one of these works, a large mandolin is suspended against an ambiguous setting along with workman's tools: a handsaw, a length of rope, and a pair of tongs. The white lines in the background, which may be interpreted as either a horizon line or a table edge, create spatial ambiguity. The mysterious symbols throughout the painting and the stark contrast between a musical instrument suitable for an elegant drawing room and rugged implements used for manual labor make this painting one of the artist's most surreal, enigmatic works.
Surrealism's interest in the artistic unconscious held little appeal for Davis, whose foremost concern was a system of color and design. Nevertheless, Davis did know and admire the work of Joan Miró, the Spanish surrealist. The cryptic configurations in Miró's paintings probably attracted Davis in his search for sophisticated formal patterns, while Miró's depiction of apparently unrelated objects appealed to his sense of the absurd. Certain elements in Still Life with Saw, such as its opaque, brown background, the arrow, and the mandolin handle transformed into an arm, the twisted, frayed rope may have been inspired by Miró paintings Davis could have seen. Close ties also exist to works by Arthur Dove, whose collages may have directly inspired Davis's work, which appears to be an interpretation of one of Dove's assemblages. Both artists included items such as a frayed rope and pieces of bent and twisted metal. In Still Life with Saw, Davis altered motifs and techniques from surrealism, which at the time was at the height of its influence in Paris, The painting contrasts significantly in intent with his earlier painting, Egg Beater No. 4, in the inclusion of recognizable objects in this painting, as opposed to the abstraction of the forms in Egg Beater No. 4. The fact that here the saw is given equal billing with the mandolin and even appears to threaten it with its emphatic jagged teeth possibly reflects the artist's opinion that utilitarian, everyday objects are as worthy of representation as traditionally used cubist motifs.