Not officially.
However, the Mint has struck coins for other countries over the years. There have been many instances where a blank (technically called a "planchet") for a foreign coin accidentally got mixed in with blanks for U.S. coins and was struck with an American design, resulting in a planchet error.
The metal disc used to make a coin is called a "coin blank" or, more formally, a "planchet." They also used to be called "flans," but that term is no longer as widely used.
Information about Mexican coins and currency, both past and present, can be found at Coin Quest, Coin Rack and Coinflation. The World of Coins website has images of Mexican currency that can be used as a reference.
Argentina, Brazil, Mexico, Peru, and Portugal all made a 1957 10 Centavos coin, but only Mexico used the word Diez on the coin. A 1957 Mexican 10 Centavos coin is only worth $0.40US even if like new.
Occasionally, the Royal mint has a mix up with the dies or the blanks used to produce coins. It is possible that the 10 New Pence dies were used on a 2 New Pence blank. If this is the case, part of the 10 Pence coin design will be outside the perimeter of the 2 Pence blank, the 10 Pence coin being slightly larger than the 2 Pence coin. Alternatively, you may have a trick coin available from magic shops.
Coin relief refers to the raised design or image on a coin that stands out from the background. It is achieved by using a die with the desired design that stamps the image onto a blank coin. The level of relief can vary depending on the design and the technique used in minting the coin.
The technical name for a coin blank is "planchet" or "flan". In common use, the word planchet generally is used for a coin blank that's been punched from a flat sheet of metal but has had no other changes. After that the blank usually goes through one or more preparatory steps before the design is added. Blanks are put into an "upsetting machine" that squeezes the circumference very slightly to produce the raised edge you see on the rim. These partially-processed blanks are more frequently called flans, although to again be technically correct a blank without a raised edge is also referred to as a Type I flan while one with the edge is Type II. Once the raised edge has been added the coin blank is fed into the press that strikes the front and back designs into the metal and, if appropriate, adds reeding or other tactile features to the edge. Once it receives its images the planchet has become a coin.
More information is needed. What do you mean by "no head" - is the front of the coin blank, or does it have a different portrait than the one you're used to seeing? What is the coin's date, if it's shown? Please post a new question with that info so your coin can be ID'ed.
Planchets are blank metal discs used in coin production. They are used as the base to create coins by stamping the design onto them. Planchets are manufactured with precise specifications to ensure uniformity in the final coins.
The blank tiles can be used as any letter.
Blank = base.
Blank = base.
You have what's called an off-center strike. The error occurs when a coin blank (planchet) doesn't center itself correctly in the collar used to hold the blank while the press strikes the images on the front and back. The more off-center the coin, the more it's worth, so my guess would be that your coin is worth no more than a couple of dollars. It's still interesting to have as a conversation piece, however.