How do I get Composer to download the latest commit in the master branch from GitHub for a package?

There is only one way to grab the head of the repository:

"require": { "behat/mink-selenium2-driver" : "dev-master" }
"minimum-stability": "dev"

Oh well, at least two ways:

"require": { "behat/mink-selenium2-driver" : "dev-master as 1.1.x-dev" }
"minimum-stability": "dev"

Probably at least three ways:

"require": { "behat/mink-selenium2-driver" : "dev-master#2e73d8134ec8526b6e742f05c146fec2d5e1b8d6" }
"minimum-stability": "dev"

Because that repository actually aliased the master branch as 1.1.x-dev, this would also work without the minimum-stability affecting all other packages:

"require": { "behat/mink-selenium2-driver" : "1.1.*@dev" }

Simply specify the master branch:

composer require --dev behat/mink-selenium2-driver:dev-master

PS: the --dev is just to specify it's a test/development requirement, that's probably what you want.