This paper presents an approach that combines the generalized multimode nonlinear Schrodinger equation with a transmission model to analyze spatiotemporal characteristics of multimode interference in single mode/large mode area fiber-graded-index multimode fiber-single mode fiber (SMF/LMA-GIMF-SMF) structures for the first time. Approximated self-imaging (ASIM) behavior in GIMF and the study of the latter structure used in spatiotemporal mode-locked fiber lasers are first demonstrated. Simulations show that these structures can work as saturable absorbers enabling high-energy pulse output due to nonlinear intermodal interactions and intensity-dependent multimode interference. Otherwise, underlying ASIM is proven that it can perturb the transmission of SMF/LMA-GIMF-SMF, causing instability of their saturable-absorption characteristics. This paper provides a theoretical guide for many applications, such as beam shaping, mode conversion, and high-energy ultrafast fiber laser.