The clockwork mechanism, which can naturally explain the origin of small numbers, is implemented in $SO(10)$ grand unified theories to address the origin of hierarchies in fermion masses and mixings. We show that a minimal Yukawa sector involving a $1{0}_{H}$ and ${\overline{126}}_{H}$ of Higgs bosons, extended with two clockwork chains consisting of $16+\overline{16}$ vectorlike fermions, can explain the hierarchical patterns with all the Yukawa couplings being of order one. Emergence of a realistic mass spectrum does not require any symmetry that distinguishes the three generations. We develop clockwork-extended $SO(10)$ GUTs both in the context of SUSY and non-SUSY frameworks. Implementation of the mechanism in non-SUSY scenario assumes a Peccei-Quinn symmetry realized at an intermediate scale, with the clockwork sector carrying nontrivial charges, which solves the strong $CP$ problem and provides axion as a dark matter candidate.