We present PepTune, a multi-objective discrete diffusion model for the simultaneous generation and optimization of therapeutic peptide SMILES. Built on the Masked Discrete Language Model (MDLM) framework, PepTune ensures valid peptide structures with state-dependent masking schedules and penalty-based objectives. To guide the diffusion process, we propose a Monte Carlo Tree Search (MCTS)-based strategy that balances exploration and exploitation to iteratively refine Pareto-optimal sequences. MCTS integrates classifier-based rewards with search-tree expansion, overcoming gradient estimation challenges and data sparsity. Using PepTune, we generate diverse, chemically modified peptides simultaneously optimized for multiple therapeutic properties, including target binding affinity, membrane permeability, solubility, hemolysis, and non-fouling for various disease-relevant targets. In total, our results demonstrate that MCTS-guided masked discrete diffusion is a powerful and modular approach for multi-objective sequence design in discrete state spaces.