Earlier this month, the Mets also added right-handed reliever Manny Alvarez to their 40-man roster.
Lutz, 24, overcame injuries this season to advance all the way to Triple-A Buffalo, batting a combined .287 with 19 home runs over four levels of the Minors. Fellow third baseman David Wright continues to block Lutz's path to the big leagues, so his shot may ultimately have to come with another organization.
Valdespin, 22, finished seventh in the Arizona Fall League with a .355 average, knocking in 19 runs and stealing seven bases in 19 games. His stint there was shortened due to injury. The Mets originally signed Valdespin as a 19-year-old out of the Dominican Republic in 2007.
Rodriguez, 22, went 8-9 for Class A Savannah. Another Dominican native, Rodriguez signed as an international free agent back in '07.
Stinson, 22, posted a 2.57 ERA during a brief callup to Buffalo late this season, after going 9-3 with a 4.24 ERA for Double-A Binghamton.
The Mets' 40-man roster now stands at 37 players, though in effect it is at 38. Francisco Rodriguez, who finished last season on the Disqualified List, does not currently count against the roster tally.
Friday's moves occurred to protect Lutz, Valdespin, Rodriguez and Stinson from the Rule 5 Draft. Any player who signed before the age of 19 and has played five professional seasons, or who signed after his 19th birthday with four professional seasons, is eligible to be selected in next month's Draft if not on the big league 40-man roster. The selecting team must pay a $50,000 fee and keep the draftee on its active roster for the entire season, with few exceptions.
Because they don't figure to be major players in the free-agent market, the Mets don't necessarily need many open spots on their 40-man roster. In addition, New York figures to gain two more spots from John Maine and Sean Green, both of whom are candidates to be non-tendered next month.