As a powerful molecular detection approach, tip-enhanced Raman scattering (TERS) spectroscopy has the advantages of nanoscale spatial resolution, label-free detection and high enhancement factor, therefore has been widely used in fields of chemistry, materials and life sciences. A TERS system enhanced by the focused gap-plasmon mode composed of Surface Plasmon Polariton (SPP) focus and the metal probe has been reported, however, its underlying enhancement mechanism for Raman excitation and scattering remains to be deeply explored. Here, we focus on the different performances of optical focus and SPP focus in the TERS system, and verify that the cooperation of these two focuses can produce maximum enhancement in a local electromagnetic field. Further, the Purcell effect on sample scattering in such a system is studied for the enhancement of Raman scattering collection in the far field. Finally, the local field enhancement and the sample far-field scattering enhancement are combined to show a full view of the whole process of TERS enhancement. This research can be applied to optimize the excitation and collection of Raman signals in TERS systems, which is of great value for the research and development of TERS technology.