Abstract Soliton frequency combs generated in microresonators offer powerful tools for optical metrology, due to the high time‐frequency resolution. Here, via exciting the intracavity Brillouin laser in a high Q monolithic fiber resonator, a pair of orthogonal Kerr soliton combs is generated, which share the same repetition ( f rep ≈ 1.001 GHz) due to the soliton trapping but different central wavelengths (≈ 9.278 GHz). They offer rich dual‐comb beat notes with minimum phase noise down to −166.5 dBc Hz −1 @1 MHz. Thanks to the geometric flexibility of the monolithic fiber resonator, the orthogonal soliton pair is found to be mechanically controllable with high precision. Specifically, by applying external stress on the microcavity in a range of ≈ 0–7.33 mN, the difference of their carrier‐envelope‐offset frequencies (Δ f ceo ) is linearly tunable with a response of 0.3 kHz µN −1 , meanwhile, tunability of the f rep reaches 0.4 kHz µN −1 . Such an orthogonally polarized dual soliton with stress controllability combining Brillouin excitation and parametric oscillation can offer a miniature all‐in‐fiber tool for wide applications ranging from frequency‐adjustable photonic microwave sources to highly sensitive gyroscopes.