In finetuning a large pretrained model to downstream tasks, parameter-efficient fine-tuning (PEFT) methods can effectively finetune pretrained models with few trainable parameters, but suffer from high GPU memory consumption and slow training speed. Because learnable parameters from these methods are entangled with the pretrained model, gradients related to the frozen pretrained model's parameters have to be computed and stored during finetuning. We propose Low-rank Attention Side-Tuning (LAST), which disentangles the trainable module from the pretrained model by freezing not only parameters but also outputs of the pretrained network. LAST trains a side-network composed of only low-rank self-attention modules. By viewing the pretrained model as a frozen feature extractor, the side-network takes intermediate output from the pretrained model and focus on learning task-specific knowledge. We also show that LAST can be highly parallel across multiple optimization objectives, making it very efficient in downstream task adaptation, for example, in finding optimal hyperparameters. LAST outperforms previous state-of-the-art methods on VTAB-1K and other visual adaptation tasks with roughly only 30\% of GPU memory footprint and 60\% of training time compared to existing PEFT methods, but achieves significantly higher accuracy.