Job scheduling for a MapReduce cluster has been an active research topic in recent years. However, measurement traces from real-world production environment show that the duration of tasks within a job vary widely. The overall elapsed time of a job, i.e. the so-called flowtime, is often dictated by one or few slowly-running tasks within a job, generally referred as the "stragglers". The cause of stragglers include tasks running on partially/intermittently failing machines or the existence of some localized resource bottleneck(s) within a MapReduce cluster. To tackle this online job scheduling challenge, we adopt the task cloning approach and design the corresponding scheduling algorithms which aim at minimizing the weighted sum of job flowtimes in a MapReduce cluster based on the Shortest Remaining Processing Time scheduler (SRPT). To be more specific, we first design a 2-competitive offline algorithm when the variance of task-duration is negligible. We then extend this offline algorithm to yield the so-called SRPTMS+C algorithm for the online case and show that SRPTMS+C is $(1+ε)-speed$ $o(\frac{1}{ε^2})-competitive$ in reducing the weighted sum of job flowtimes within a cluster. Both of the algorithms explicitly consider the precedence constraints between the two phases within the MapReduce framework. We also demonstrate via trace-driven simulations that SRPTMS+C can significantly reduce the weighted/unweighted sum of job flowtimes by cutting down the elapsed time of small jobs substantially. In particular, SRPTMS+C beats the Microsoft Mantri scheme by nearly 25% according to this metric.