Modeling protein sequences as a language has made language models a powerful tool in computational biology, yet the language itself remains poorly understood. A key step toward understanding it is identifying its constituent units. In natural languages, morphemes can occur in multiple forms; similarly, in proteins, mutations can give rise to variations of a unit that persist through evolution, forming families of related units. We introduce PUMA (Protein Units via Mutation-Aware Merging), an algorithm that learns protein units from sequence and explores their mutational variants using substitution matrices, forming a genealogy of unit families. Our results show that mutations remaining within a PUMA family are more often benign than the substitution matrix alone predicts, and that PUMA genealogy improves molecular function representations compared to treating units independently. A case study of a unit family demonstrates relatedness beyond homology. PUMA achieves competitive performance on downstream tasks when used as a protein language model tokenizer. Moreover, collapsing units into families results in a smaller embedding table and faster training. Together, these results support PUMA as a biologically grounded protein vocabulary that organizes protein units into plausible families of mutational variants. The source code is available at https://github.com/boun-tabi-lifelu/PUMA.