It has been shown by many researchers that transformers perform as well as convolutional neural networks in many computer vision tasks. Meanwhile, the large computational costs of its attention module hinder further studies and applications on edge devices. Some pruning methods have been developed to construct efficient vision transformers, but most of them have considered image classification tasks only. Inspired by these results, we propose SiDT, a method for pruning vision transformer backbones on more complicated vision tasks like object detection, based on the search of transformer dimensions. Experiments on CIFAR-100 and COCO datasets show that the backbones with 20\% or 40\% dimensions/parameters pruned can have similar or even better performance than the unpruned models. Moreover, we have also provided the complexity analysis and comparisons with the previous pruning methods.