In prior arts, when it is necessary to separate and detect circulating tumor cells (CTC) in the blood of a living animal (including a human body), cell sorting and counting are performed by drawing a certain volume of blood and then using a method such as the density gradient centrifugation. The density gradient centrifugation method uses a certain medium to form a continuous or discontinuous density gradient in a centrifugal tube, places the cell suspension or homogenate on top of the medium, and sorts the cells through gravity or centrifugal force field effects. Its disadvantages are as below: 1. due to the limitation of the centrifuge, it is impossible to simultaneously perform centrifugation on a large volume of the cell suspension and thereby separate the cells, and the efficiency is low; 2. the added medium may affect the cell activity and the property of the solution, and operations of removing the medium are time-consuming and labored; 3. the operation is complicated and has a high requirement on the medium configuration. Hence, a new device and method for separating and detecting the number of the circulating tumor cells in the blood of a living animal is needed in this field. In recent years, a method of separating the circulating tumor cells in the blood by using a track-etched membrane appears in this field. For example, “Preparation of polycarbonate nuclear track microfilters and their applications” by Huanhua CUI, Shicheng WANG, et al. discloses using a track microporous filter membrane to diagnose the circulating tumor cells in the blood, specifically, putting the circulating tumor cells retained on the track microporous filter membrane to be observed under a microscope. The inventor of the present disclosure also uses this membrane to separate the circulating tumor cells in the blood of some living animals (for example, rabbits), and diagnoses and counts the circulating tumor cells. However, a device corresponding to this method may only be able to separate the circulating tumor cells in very small portion of blood of the living animal at a time, and cannot effectively separate the circulating tumor cells in most or all of the blood of the living animal. In particular, for a larger living animal (for example, a human body), such defect is particularly significant. The reason is that, in order to maintain the living animal in a normal living state, it is impossible to evacuate all the blood from the living animal to separate the circulating tumor cells; otherwise the individual will die. In addition, because the number of the circulating tumor cells (CTC) in the blood is extremely small, the sensitivity of the separation and detection may be greatly reduced (the detection result may be incorrect easily) if only a small volume of the blood of the living animal is drawn to perform the separation and detection; but increase of the volume of the blood for processing may threaten the healthy and life of the living animal. Therefore, it is further necessary to provide a new device and method for separating and detecting the circulating tumor cells in a living animal (including a human body) in this field.