How do we explain mutations, in the deterministic world of chemical reactions?
The topic is much larger than a scope for a single answer. But staying at general, low level chemical principles, it can be pinned down to several mechanisms leading to possible mutations:


Chemical reactions are not deterministic. Generally, on molecular level, there is less than 100% probability the desired and expected reaction happens, and more than 0%  probability it does not happen, or other reaction happens.
A molecule may react with other molecule in more than one way, with alternative reactions having their probability to form  "by-products".
A molecule may react with similar, but still native molecule, that it is not supposed to react with to form desired product.
A molecule may react with a molecule that should not be present, coming e.g. from pollution, medical treatment or poisoning.
Some foreign molecules may not react directly, but can affect DNA replication or synthesis of RNA or proteins.
A molecule may be broken by ionizating irradiation like UV, X-ray or  $\gamma$ photons, high energy subatomic particles or ions from the natural body radioactivity ($\ce{^{14}C}$, $\ce{^{40}K}$), from natural radioactive background ($\ce{U}$, $\ce{Ra}$, $\ce{Rn}$), from pollution (radioctive elements from coal burning ), medical treatment, radiation incidents or even poisoning.