Processing-using-DRAM (PUD) is a processing-in-memory (PIM) approach that uses a DRAM array's massive internal parallelism to execute very-wide data-parallel operations, in a single-instruction multiple-data (SIMD) fashion. However, DRAM rows' large and rigid granularity limit the effectiveness and applicability of PUD in three ways. First, since applications have varying degrees of SIMD parallelism, PUD execution often leads to underutilization, throughput loss, and energy waste. Second, most PUD architectures are limited to the execution of parallel map operations. Third, the need to feed the wide DRAM row with tens of thousands of data elements combined with the lack of adequate compiler support for PUD systems create a programmability barrier. Our goal is to design a flexible PUD system that overcomes the limitations caused by the large and rigid granularity of PUD. To this end, we propose MIMDRAM, a hardware/software co-designed PUD system that introduces new mechanisms to allocate and control only the necessary resources for a given PUD operation. The key idea of MIMDRAM is to leverage fine-grained DRAM (i.e., the ability to independently access smaller segments of a large DRAM row) for PUD computation. MIMDRAM exploits this key idea to enable a multiple-instruction multiple-data (MIMD) execution model in each DRAM subarray. We evaluate MIMDRAM using twelve real-world applications and 495 multi-programmed application mixes. Our evaluation shows that MIMDRAM provides 34x the performance, 14.3x the energy efficiency, 1.7x the throughput, and 1.3x the fairness of a state-of-the-art PUD framework, along with 30.6x and 6.8x the energy efficiency of a high-end CPU and GPU, respectively. MIMDRAM adds small area cost to a DRAM chip (1.11%) and CPU die (0.6%).