  We prove that the supersymmetric deformed $ \mathbb{CP}^{1} $ sigma model
(the generalization of the Fateev-Onofri-Zamolodchikov model) admits an
equivalent description as a generalized Gross-Neveu model. This formalism is
useful for the study of renormalization properties and particularly for
calculation of the one- and two-loop $ \beta $-function. We show that in the UV
the superdeformed model flows to the super-Thirring CFT, for which we also
develop a superspace approach. It is then demonstrated that the super-Thirring
model is equivalent to a sigma model with the cylinder $ \mathbb{R} \times
S^{1} $ target space by an explicit computation of the correlation functions on
both sides. Apart from that, we observe that the original model has another
interesting conformal limit, given by the supercigar model, which as well could
be described in the Gross-Neveu approach.
