Recent graph-based models for multi-intent SLU have obtained promising results through modeling the guidance from the prediction of intents to the decoding of slot filling. However, existing methods (1) only model the unidirectional guidance from intent to slot, while there are bidirectional inter-correlations between intent and slot; (2) adopt homogeneous graphs to model the interactions between the slot semantics nodes and intent label nodes, which limit the performance. In this paper, we propose a novel model termed Co-guiding Net, which implements a two-stage framework achieving the mutual guidances between the two tasks. In the first stage, the initial estimated labels of both tasks are produced, and then they are leveraged in the second stage to model the mutual guidances. Specifically, we propose two heterogeneous graph attention networks working on the proposed two heterogeneous semantics-label graphs, which effectively represent the relations among the semantics nodes and label nodes. Besides, we further propose Co-guiding-SCL Net, which exploits the single-task and dual-task semantics contrastive relations. For the first stage, we propose single-task supervised contrastive learning, and for the second stage, we propose co-guiding supervised contrastive learning, which considers the two tasks' mutual guidances in the contrastive learning procedure. Experiment results on multi-intent SLU show that our model outperforms existing models by a large margin, obtaining a relative improvement of 21.3% over the previous best model on MixATIS dataset in overall accuracy. We also evaluate our model on the zero-shot cross-lingual scenario and the results show that our model can relatively improve the state-of-the-art model by 33.5% on average in terms of overall accuracy for the total 9 languages.