Mini pocket knives are only legal to carry in certain locations and under certain contexts. For example, when boarding a plane in the United States, all kinds of knives are completely disallowed and carry civil penalties, unless they are made of plastic or have a rounded butter-knife edge.
In California, knives of any size are legal, as long as they are not designed to be undetectable. For example, a plastic mini pocket knife that can't be picked up by metal detectors would be illegal, as would a mini pocket knife that is designed to look like another object, such as a lipstick tube.
In Texas, pocket knives and knives with short blades are explicitly legal. However, gravity knives are illegal, so a mini pocket knife in Texas would have to opened using some other mechanism.
In New York City, pocket knives with blades less than 4 inches long are technically legal. However, as of 2016, actual enforcement designates many mini pocket knives as illegal, since the law interprets knives with weak folding mechanisms as illegal gravity knives.