"Tamper" implies action taken with intend to improperly change the meaning. "Alter" simply means "change". "Mutilate" simply means "damage" but in this context implies "Make unreadable". "Obliterates" here means 'make unreadable" or "remove".
As a practical matter, there is not much if any difference between these words in this context, and no authority will spend any time at all considering whether some action is 'tampering" or "mutilation". The word "or" is used precisely to avoid such arguments. Any of these shades of meaning is equally forbidden.
English-language laws and regulations often specify multiple synonyms or near-synonyms , connecting them with "or" so that anything within the more general scope of the concept is included. Charles Rembar, in his book The Law of the Land, asserted that this dated to the period in England shortly after the Norman Conquest, and that lawyers tended to include equivalent terms from Latin, Norman French, and English. He mentions such combinations as "Give, devise, and bequeath" and "Promise, covenant, and agree" as typical and often-used examples of this tendency.
When this sort of multiple terminology is used, it is generally only useful to try to understand what is covered by the combined phrase, and of no value to try to determine which term covers which part of the concept.
In the cited cases, anyone who tries to change a passport to say something that the government didn't intend, or who tries to damage or destroy a passport, or anything similar, would be guilty of the forbidden act. And similarly, anyone who tries to make an MVID read differently, or to make it unreadable, would be guilty.