Compact cesium beam clocks are major frequency references for deployable timing systems. However, further improvement of their short-term frequency stability is limited by the clock signal-to-noise ratio (SNR). Although two-laser optical pumping can increase the effective atomic utilization, the achievable clock SNR has long been limited by laser-induced frequency-to-amplitude noise conversion. Here, we demonstrate a compact dual-Faraday-laser-pumped (DFP) Cs beam clock enabled by a low-frequency-noise atom-referenced laser architecture. The intracavity Faraday anomalous dispersion optical filter provides inherent alignment to the Cs D₂ resonances, while modulation transfer spectroscopy offers suppressed frequency noise and drift. The resulting laser system supports robust turnkey operation with a Lorentzian linewidth of 2.12 kHz. The DFP Cs clock achieves a clock SNR of 46,365 in a 1-Hz bandwidth and a fractional Allan deviation of 7.7× 10⁻¹³/√τ , with Hadamard deviation reaching 7.7× 10⁻¹⁵ at 10,000 s. This work pushes the fractional frequency stability of a compact Cs beam clock into the 10⁻¹³/√τ regime, providing a pathway toward high-performance Cs frequency references for field-deployable precision timing, navigation, and synchronization.