What is claimed is:1. A method for manufacturing a flexible display device, comprising:forming a layer of flexible display devices on a support plate;etching the layer of flexible display devices on the support plate to expose a portion of the support plate at a cutting region, the cutting region being a predetermined region between two adjacent flexible display devices; andremoving the layer of flexible display devices from the support plate after the etching process, so as to obtain a plurality of flexible display devices separated from each other,wherein forming the layer of flexible display devices on the support plate comprises:forming a flexible substrate on the support plate; andforming a plurality of layers on the flexible substrate, wherein the cutting region is covered by the flexible substrate and the plurality of layers;wherein each of the plurality of flexible display devices on the support plate comprises a bending region covered by the flexible substrate and the plurality of layers;wherein forming the plurality of layers on the flexible substrate comprises forming a Thin Film Transistor (TFT) array layer on the flexible substrate, wherein the TFT array layer comprises a gate electrode layer, a source electrode layer and a drain electrode layer;wherein etching the layer of flexible display devices on the support plate so as to expose the portion of the support plate at the cutting region comprises removing a portion of the TFT array layer at the cutting region and a portion of the TFT array layer at the bending region through a single etching process.2. The method according to claim 1, wherein forming the plurality of layers on the flexible substrate comprises:forming an etch stop layer, wherein the etch stop layer comprises a first barrier pattern and a second barrier pattern arranged at two sides of the cutting region respectively to define an etching width.3. The method according to claim 2, wherein forming the plurality of layers on the flexible substrate comprises:forming the etch stop layer and the gate electrode layer of the TFT array layer through a single patterning process; orforming the etch stop layer and the source electrode layer and the drain electrode layer of the TFT array layer through a single patterning process.4. The method according to claim 2, wherein the etch stop layer comprises a first metal layer and a second metal layer, andforming the plurality of layers on the flexible substrate comprises:forming the first metal layer of the etch stop layer and the gate electrode layer of the TFT array layer through a first patterning process; andforming the second metal layer of the etch stop layer and the source electrode layer and the drain electrode layer of the TFT array layer through a second patterning process.5. The method according to claim 2, wherein prior to forming the TFT array layer on the flexible substrate, the method further comprises forming a buffer layer on the flexible substrate.6. The method according to claim 2, wherein each of the plurality of flexible display devices on the support plate comprises a bending region covered by the flexible substrate and the plurality of layers.7. The method according to claim 1, wherein forming the plurality of layers on the flexible substrate comprises forming an organic material layer on the TFT array layer.8. The method according to claim 7, wherein forming the plurality of layers on the flexible substrate comprises forming an encapsulation layer on the organic material layer.9. The method according to claim 8, wherein etching the layer of flexible display devices to expose the portion of the support plate at the cutting region comprises etching off a portion of the plurality of layers and a portion of the flexible substrate, so as to expose the portion of the support plate at the cutting region.10. The method according to claim 7, wherein etching the layer of flexible display devices on the support plate so as to expose the portion of the support plate at the cutting region comprises removing a portion of the organic material layer at the cutting region and a portion of the organic material layer at the bending region through an exposing process.11. The method according to claim 1, wherein subsequent to removing the portion of the TFT array layer at the cutting region and the portion of the TFT array layer at the bending region through a single etching process, the method further comprises removing a portion of the buffer layer at the cutting region and a portion of the buffer layer at the bending region through a single etching process.12. The method according to claim 11, wherein subsequent to the removing the portion of the buffer layer at the cutting region and the portion of the buffer layer at the bending region through a single etching process, the method further comprises removing a portion of the encapsulation layer and a portion of the flexible substrate at the cutting region and a portion of the encapsulation layer at the bending region through a single etching process, so as to expose the portion of the support plate at the cutting region.13. The method according to claim 12, wherein the flexible substrate comprises a first flexible substrate, an isolation layer and a second flexible substrate laminated in turn, wherein the removing the portion of the encapsulation layer and the portion of the flexible substrate at the cutting region and the portion of the encapsulation layer at the bending region through a single etching process comprises removing the portion of the encapsulation layer at the cutting region, the portion of the encapsulation layer at the bending region, and a portion of each of the second flexible substrate, the isolation and the first flexible substrate at the cutting region through a single etching process.14. The method according to claim 1, wherein removing the layer of flexible display devices from the support plate after the etching process comprises removing the layer of flexible display devices from the support plate through a laser lift off process.15. A flexible display device manufactured through the method according to claim 1.