Transactional stream processing engines (TSPEs) have gained increasing attention due to their capability of processing real-time stream applications with transactional semantics. However, TSPEs remain susceptible to system failures and power outages. Existing TSPEs mainly focus on performance improvement, but still face a significant challenge to guarantee fault tolerance while offering high-performance services. We revisit commonly-used fault tolerance approaches in stream processing and database systems, and find that these approaches do not work well on TSPEs due to complex data dependencies. In this paper, we propose a novel TSPE called MorphStreamR to achieve fast failure recovery while guaranteeing low performance overhead at runtime. The key idea of MorphStreamR is to record intermediate results of resolved dependencies at runtime, and thus eliminate data dependencies to improve task parallelism during failure recovery. MorphStreamR further mitigates the runtime overhead by selectively tracking data dependencies and incorporating workload-aware log commitment. Experimental results show that MorphStreamR can significantly reduce the recovery time by up to 3.1 x while experiencing much less performance slowdown at runtime, compared with other applicable fault tolerance approaches.