In parallel process latent growth curve mediation models, the mediation pathways from treatment to the intercept or slope of outcome through the intercept or slope of mediator are often of interest. In this study, we developed causal mediation analysis methods for these mediation pathways. Particularly, we provided causal definitions and identification results for the interventional indirect effects via the mediator intercept (or slope) alone and due to their mutual dependence. For estimation, we proposed an interaction model that incorporates interactions among the mediator intercept/slope and treatment, coupled with a Bayesian method. We evaluated the studied methods through simulations, and illustrated their applications using an empirical example.