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In the present work, a deterministic approach is applied for the first time ever to simulate the rarefied gas flow in the particle exhaust system of a nuclear fusion device. As an example of such a system, the pumping area of the DEMO (DEMOnstration Fusion Power Plant) fusion reactor is considered, which is characterized by high geometrical complexity and strong gradients of macroscopic quantities. The Knudsen number in this system may vary from free molecular up to the slip regime and the flow behavior must be described by the Boltzmann equation. In the present work, the Boltzmann equation is approximated by the well-known Bhatnagar–Gross–Krook and Shakhov kinetic models supplemented with the deterministic discrete velocity method. In addition, in order to assess the capabilities of the deterministic modeling, the problem has also been studied by solving the Boltzmann equation with the stochastic direct simulation Monte Carlo (DSMC) method. Extended comparisons between the deterministic and stochastic methods in terms of all macroscopic quantities of practical interest, namely, pressure, number density, temperature, and pumping fluxes, are performed and remarks about the effectiveness of the implemented deterministic approach have been drawn. Results are obtained by assuming He and D2 gas flows, various values of the capture coefficient at the pumping opening, and two different scenarios of the inlet gas temperature. In all examined cases, the deterministic results are in very good agreement with the DSMC ones, with the maximum relative deviation being less than 4%. The nonlinear deterministic code is significantly faster than the stochastic DSMC code for acceptable noise levels. The pumping fluxes and the pressure values in the vicinity of the pumping opening, both quantities useful for pumping system evaluation, have been calculated in terms of the capture coefficient. The present work may support decision making on the suitability of the pumping technology of DEMO and the design of the pumping system.