Process raspberries in a food processor until smooth, stopping once to scrape down sides. Pour puree through a fine wire-mesh strainer, pressing with the back of a spoon; discard seeds. Add enough milk to equal 1/2 cup.
Beat butter at medium speed with an electric mixer until fluffy. Gradually add powdered sugar alternately with raspberry mixture, beginning and ending with powdered sugar. Beat at low speed until blended after each addition.