Spam poses a growing threat to blockchain networks. Adversaries can easily create multiple accounts to flood transaction pools, inflating fees and degrading service quality. Existing defenses against spam, such as fee markets and staking requirements, primarily rely on economic deterrence, which fails to distinguish between malicious and legitimate users and often exclude low-value but honest activity. To address these shortcomings, we present StarveSpam, a decentralized reputation-based protocol that mitigates spam by operating at the transaction relay layer. StarveSpam combines local behavior tracking, peer scoring, and adaptive rate-limiting to suppress abusive actors, without requiring global consensus, protocol changes, or trusted infrastructure. We evaluate StarveSpam using real Ethereum data from a major NFT spam event and show that it outperforms existing fee-based and rule-based defenses, allowing each node to block over 95% of spam while dropping just 3% of honest traffic, and reducing the fraction of the network exposed to spam by 85% compared to existing rule-based methods. StarveSpam offers a scalable and deployable alternative to traditional spam defenses, paving the way toward more resilient and equitable blockchain infrastructure.