To alleviate hardware scarcity in training large deep neural networks (DNNs), particularly large language models (LLMs), we present FusionLLM, a decentralized training system designed and implemented for training DNNs using geo-distributed GPUs across different computing clusters or individual devices. Decentralized training faces significant challenges regarding system design and efficiency, including: 1) the need for remote automatic differentiation (RAD), 2) support for flexible model definitions and heterogeneous software, 3) heterogeneous hardware leading to low resource utilization or the straggler problem, and 4) slow network communication. To address these challenges, in the system design, we represent the model as a directed acyclic graph of operators (OP-DAG). Each node in the DAG represents the operator in the DNNs, while the edge represents the data dependency between operators. Based on this design, 1) users are allowed to customize any DNN without caring low-level operator implementation; 2) we enable the task scheduling with the more fine-grained sub-tasks, offering more optimization space; 3) a DAG runtime executor can implement RAD withour requiring the consistent low-level ML framework versions. To enhance system efficiency, we implement a workload estimator and design an OP-Fence scheduler to cluster devices with similar bandwidths together and partition the DAG to increase throughput. Additionally, we propose an AdaTopK compressor to adaptively compress intermediate activations and gradients at the slowest communication links. To evaluate the convergence and efficiency of our system and algorithms, we train ResNet-101 and GPT-2 on three real-world testbeds using 48 GPUs connected with 8 Mbps~10 Gbps networks. Experimental results demonstrate that our system and method can achieve 1.45 - 9.39x speedup compared to baseline methods while ensuring convergence.