Multimodal sarcasm detection requires reasoning over cross-modal incongruities between literal expression and intended meaning, yet the specific analytical perspectives needed vary across samples due to the diversity of sarcastic mechanisms. While recent methods make this analytical process explicit, they still rely on fixed, predefined perspectives that operate independently under hand-crafted routing rules. We argue that multimodal sarcasm detection instead calls for self-elicited multi-perspective reasoning, where a model autonomously generates the perspectives needed for each sample and progressively integrates them into a coherent analysis. To realize this goal, we propose ProCrit, a Proposal-Critic two-agent framework with a proposal agent for multi-perspective reasoning and a critic agent for external evaluation and targeted revision guidance. First, to overcome the lack of process-level supervision in existing sarcasm datasets, ProCrit synthesizes process-level reasoning annotations through a dynamic-role agentic rollout: a strong vision-language model sequentially spawns analytical roles within a shared context, and the resulting multi-role trajectories are flattened into sequences that preserve cross-perspective dependencies while enabling efficient autoregressive generation. Second, to improve reasoning reliability, ProCrit adopts a draft-critique-revise paradigm in which an independent critic identifies reasoning deficiencies and provides targeted natural-language feedback for directed revision. Finally, we develop a mutual-refinement training framework that jointly optimizes proposal drafting and feedback-guided revision via dual-stage reinforcement learning, while refining the critic agent according to the actual effectiveness of its feedback. Experiments on three widely used benchmarks demonstrate the effectiveness of ProCrit.