Mitch Winehouse kicked off the US launch of the Amy Winehouse Foundation, the nonprofit founded nine months ago in honor of his tragic musician daughter. On Wednesday, Mitch, with Amy’s mother, Janis, and their son, Alex, hosted an event at Joe’s Pub in the East Village — poignant, as Amy played her first US gig there in 2007. Mitch, a singer himself, performed four songs with a jazz band. The grieving father will publish a book in June about Amy, who died of alcohol poisoning last year at age 27, titled, “Amy, My Daughter.” All proceeds from the HarperCollins release will benefit the foundation. Its UK branch has already raised $1.6 million, and the US organization is also planning a Sept. 10 event — the Amy Winehouse Inspiration Awards and Gala — at the WaldorfAstoria, where friends of Winehouse, including Tony Bennett, will perform. After the perfomance at Joe’s Pub, the Winehouses headed for a quiet dinner at Barrio 47 with foundation chiefs and SNR Denton’s David Hryck.