An elegant and convenient rigorous approach for solving canonical circular open-ended dielectric-loaded waveguide diffraction problems is presented. It uses the solution of corresponding Wiener-Hopf-Fock equation and leads to an infinite linear system for reflection coefficients (S-parameters) of the waveguide, and the latter can be efficiently solved numerically using the reducing technique. As a specific example directly applicable to beam-driven radiation sources based on dielectric-lined capillaries, diffraction of a slow TM symmetrical mode at the open end of a circular waveguide with uniform dielectric filling is considered. A series of such modes forms the wakefield (Cherenkov radiation field) generated by a charged particle bunch during its passage along the waveguide axis. Calculated S-parameters were compared with those obtained from COMSOL simulation and an excellent agreement was shown. This method is expected to be very convenient for analytical investigation of various electromagnetic interactions of terahertz (THz) waves (both free and guided) and charged particle bunches with slow-wave structures perspective in context of modern beam-driven THz emitters, THz accelerators, and THz-based bunch manipulation and bunch diagnostic systems.