Neural implicit fields are quickly emerging as an attractive representation for learning based techniques. However, adopting them for 3D shape modeling and editing is challenging. We introduce a method for $\mathbf{E}$diting $\mathbf{I}$mplicit $\mathbf{S}$hapes $\mathbf{T}$hrough $\mathbf{P}$art $\mathbf{A}$ware $\mathbf{G}$enera$\mathbf{T}$ion, permuted in short as SPAGHETTI. Our architecture allows for manipulation of implicit shapes by means of transforming, interpolating and combining shape segments together, without requiring explicit part supervision. SPAGHETTI disentangles shape part representation into extrinsic and intrinsic geometric information. This characteristic enables a generative framework with part-level control. The modeling capabilities of SPAGHETTI are demonstrated using an interactive graphical interface, where users can directly edit neural implicit shapes.