Mexico is a failed state where agents of the state are more likely to screw you over than help you. The old Mexican knife forums I used to participate in years ago were filled with a mix of horror & success stories. A big factor is luck and location, unfortunately.
Legally speaking, Mexicans have the right to own weapons inside of their homes for self-defense, collecting, etc. EXCEPT weapons that are used by the Mexican Army(lately expanded to include ANY army). As far as blades, this includes sabers, bayonets and spears because when that law was established Mexico was in the middle of a revolution and they were still viable weapons.
As far as carrying: do not carry any blades if you are in Mexico. You can get in trouble with local police including getting fined, arrested and surely having your property "confiscated" (which I call stolen). Even a little swiss army knife. Only carry if you have a good reason to carry(going camping maybe?), carry something dirt cheap and not tactical looking and bear in mind it is up to the police officer to decide if you have a good reason to have it or not. More likely than not if you have a blade they will take it from you.
As far as importing a knife from other countries: legally(last I checked) you do not need special permission IF you are importing less than 5 pieces and they do not fall under the prohibitions mentioned above. HOWEVER, like I said, the agents of the state and mail services are likely to screw you over and request SEDENA permits that are not applicable, confiscate your property, etc.
This is what the official customs site says:
My personal experience:
Many years ago(circa 2008) I bought a Cold Steel Recon Tanto online and had it shipped to a US address close to the border. I wanted to do the right thing and verify if it was ok for me to take it to Mexico. I printed a picture of the knife along with an older version of the document above. I went to the Mexican customs, parked, and asked them with picture and document in hand if it was ok for me to bring it back to Mexico. Those prepotent illiterates said they didn't know. One suggested to just hide it under the seats(lol?) and their supervisor who didn't give a shit just said it was prohibited. So
Good luck.