Processing-using-DRAM has been proposed for a limited set of basic operations (i.e., logic operations, addition). However, in order to enable full adoption of processing-using-DRAM, it is necessary to provide support for more complex operations. In this paper, we propose SIMDRAM, a flexible general-purpose processing-using-DRAM framework that (1) enables the efficient implementation of complex operations, and (2) provides a flexible mechanism to support the implementation of arbitrary user-defined operations. The SIMDRAM framework comprises three key steps. The first step builds an efficient MAJ/NOT representation of a given desired operation. The second step allocates DRAM rows that are reserved for computation to the operation's input and output operands, and generates the required sequence of DRAM commands to perform the MAJ/NOT implementation of the desired operation in DRAM. The third step uses the SIMDRAM control unit located inside the memory controller to manage the computation of the operation from start to end, by executing the DRAM commands generated in the second step of the framework. We design the hardware and ISA support for SIMDRAM framework to (1) address key system integration challenges, and (2) allow programmers to employ new SIMDRAM operations without hardware changes. We evaluate SIMDRAM for reliability, area overhead, throughput, and energy efficiency using a wide range of operations and seven real-world applications to demonstrate SIMDRAM's generality. Using 16 DRAM banks, SIMDRAM provides (1) 88x and 5.8x the throughput, and 257x and 31x the energy efficiency, of a CPU and a high-end GPU, respectively, over 16 operations; (2) 21x and 2.1x the performance of the CPU and GPU, over seven real-world applications. SIMDRAM incurs an area overhead of only 0.2% in a high-end CPU.