What is claimed is:1. A method of fabricating a display substrate, comprising:forming a mother substrate on a support substrate;cutting the mother substrate to separate a portion of the mother substrate from a remainder of the mother substrate, thereby forming a base substrate; andsubsequent to cutting the mother substrate, forming an encapsulating layer on the base substrate for encapsulating the display substrate.2. The method of claim 1, wherein a part of the encapsulating layer is formed substantially surrounding at least a part of a side surface of the base substrate.3. The method of claim 1, wherein cutting the mother substrate is performed using a laser.4. The method of claim 1, further comprising forming a plurality of thin film transistors; wherein forming the encapsulating layer comprises depositing an encapsulating material on side of the plurality of thin film transistors distal to the base substrate.5. The method of claim 4, wherein cutting the mother substrate is performed to form the base substrate having a top surface, a bottom surface opposite to the top surface, and a side surface connecting the top surface and the bottom surface, the top surface being on a side of the bottom surface proximal to the plurality of thin film transistors;depositing the encapsulating material is performed to form the encapsulating layer having a top part and a side part connected to the top part, the top part being on a side of the plurality of thin film transistors distal to the base substrate for encapsulating the display substrate; andthe side part of the encapsulating layer is formed to encapsulate a side of the display substrate and substantially surrounds the side surface of the base substrate.6. The method of claim 4, wherein depositing the encapsulating material is performed using a mask plate having an aperture corresponding to the display substrate; anda projection of an edge of the mask plate surrounding the aperture on the support substrate is spaced apart from a projection of an edge of the base substrate on the support substrate by a distance in a range of approximately 1 μm to approximately 500 μm.7. The method of claim 4, wherein the display substrate is an organic light emitting diode display substrate;prior to depositing the encapsulating material, the method further comprising forming a plurality of organic light emitting diodes on the base substrate.8. The method of claim 7, wherein the mother substrate is formed using a flexible material.9. A display substrate, comprising:a base substrate;a plurality of thin film transistors on the base substrate;an encapsulating layer on a side of the plurality of thin film transistors distal to the base substrate for encapsulating the display substrate;a planarization layer on a side of the encapsulating layer distal to the base substrate; andan auxiliary encapsulating layer on a side of the planarization layer distal to the encapsulating layer;wherein a part of the encapsulating layer substantially surrounds at least a part of a side surface of the base substrate;the base substrate comprises a top surface, a bottom surface opposite to the top surface, and a side surface connecting the top surface and the bottom surface, the top surface being on a side of the bottom surface proximal to the plurality of thin film transistorsthe encapsulating layer comprises a top part and a side part connected to the top part, the top part being on a side of the plurality of thin film transistors distal to the base substrate for encapsulating the display substrate; andthe side part of the encapsulating layer encapsulates a side of the display substrate and substantially surrounds the side surface of the base substrate.10. The display substrate of claim 9, wherein the side part of the encapsulating layer substantially surrounds an entire perimeter of the side surface of the base substrate.11. The display substrate of claim 9, wherein the bottom surface of the base substrate constitutes a bottom surface of the display substrate.12. The display substrate of claim 9, wherein any signal line of the display substrate is on a side of the top surface distal to the bottom surface.13. The display substrate of claim 9, wherein a projection of the encapsulating layer on a plane containing the bottom surface of the base substrate substantially covers a projection of the base substrate on the plane containing the bottom surface of the base substrate.14. The display substrate of claim 9, wherein a contact interface between the encapsulating layer and the base substrate is substantially on the side surface of the base substrate.15. The display substrate of claim 9, wherein projections of the encapsulating layer and the auxiliary encapsulating layer on a plane containing the bottom surface of the base substrate substantially overlap with each other.16. The display substrate of claim 9, wherein the base substrate is a flexible base substrate.17. The display substrate of claim 9, wherein the display substrate is an organic light emitting diode display substrate further comprising a plurality of organic light emitting diodes on the base substrate and encapsulated by the encapsulating layer.18. A display apparatus, comprising the display substrate of claim 9.