We demonstrate a method to quantify and manipulate nuclear spin decoherence mechanisms that are active in zero to ultralow magnetic fields. These include (i) nonadiabatic switching of spin quantization axis due to residual background fields and (ii) scalar pathways due to through-bond couplings between 1H and heteronuclear spin species, such as 2H used partially as an isotopic substitute for 1H. Under conditions of free evolution, scalar relaxation due to 2H can significantly limit nuclear spin polarization lifetimes and thus the scope of magnetic resonance procedures near zero field. It is shown that robust trains of pulsed dc magnetic fields that apply π flip angles to one or multiple spin species may switch the effective symmetry of the nuclear spin Hamiltonian, imposing decoupled or coupled dynamic regimes on demand. The method should broaden the spectrum of hyperpolarized biomedical contrast-agent compounds and hyperpolarization procedures that are used near zero field.