Privacy preservation is highly expected in the Bitcoin Network. However, only applying pseudonyms cannot completely ensure anonymity/unlinkability between payers and payees. Current approaches mainly depend on a mixer service, which obfuscates payer-payee relationships of transactions. While the mixer service improves transaction privacy, it still suffers from some severe security threats (e.g., DoS attack and collusion attack), and does not support effective and reliable off-chain payment in a parallel mode. In this paper, we propose a mixing protocol for the Bitcoin Network based on zero-knowledge proof, called SofitMix. It is the first mixing protocol that can effectively resist both the DoS attack and the collusion attack. It can also support a set of parallel off-chain payments in a reliable way no matter whether some payers abort a transaction. We analyze and prove SofitMix security following the Universal Composability model with regard to fair exchange, unlinkability, collusion-resistance, DoS-resistance and Sybil-resistance. Through a proof-of-concept implementation, we demonstrate its validity and fairness. We also show its advance on off-chain payment reliability and DoS attack resistance, compared to TumbleBit.