Here's the link to Grinnell's web site with their recommended study abroad options.
Off-Campus Study There are literally dozens more available, that you can arrange with Grinnell.
Study abroad for American students is a huge industry overseas. Most LACs and universities have relationships with the same programs. For example, SITA in Madurai, India, appears as a program that was cited by almost every LAC we looked at, as is a year long program at the London School of Economics. In addition, Grinnell has their own programs in London and Washington DC, where you would be with other Grinnell students, and relationships with other schools (Oberlin and Hamilton) to name two that have their own programs abroad.
So in short, yes, you can study Mandarin abroad with Grinnell. Check the course catalog on line for courses offered as well.