Your question is a very complicated question. Every state has different divorce laws - similar, but different. In addition, every country has different divorce laws and with your wife living in Mexico, you will also have to explore whether a divorce in Zimbabwe would be recognized in Mexico. California would not recognize your divorce in Zimbabwe if both you and your spouse were residents of the California when you obtained your divorce.
There are several conflict of laws issues in your fact pattern and not knowing where you will be residing when you obtain your divorce it is difficult to determine if such will be valid. When considering divorce, I would encourage you not to act in haste and take into account the effect of the divorce decree, your obligations and the division of property. California is a community property state, others are not. Certainly other countries have different laws for division of property. Mexico has its own laws for division of property all that must be researched and addressed to ensure and protect your rights and obligations after the divorce.
Furthermore, since your wife and your children live in Mexico, you will need to find out if Zimbabwe can entertain any custody and visitation orders. California could not make any orders as to custody and visitation because the children are out of its jurisdiction. California could make an order for child support, but support and custody are intertwined and without a custody order you may be binding yourself to a support order that is not aligned your custody and visitation plan.
I would encourage you to consult with experienced attorneys in Mexico, Zimbawe and California (if you intend to remain here for some time) to understand what your options and obligations are after your divorce.
It is a complex fact pattern, but for the child, it might be possible. But since you have a child, even if you could do the Zimbabwe divorce, it is very unadvisable and may lead to a lot more problems than it solves.
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