Edit: Long after I wrote this post and it was accepted as the answer, the am force-stop command was implemented by the Android team, as mentioned in this answer.
Alternatively: Rather than just stopping the app, since you mention wanting a "clean slate" for each test run, you can use adb shell pm clear com.my.app.package, which will stop the app process and clear out all the stored data for that app.
If you're on Linux:
adb shell ps | grep com.myapp | awk '{print $2}' | xargs adb shell kill
That will only work for devices/emulators where you have root immediately upon running a shell. That can probably be refined slightly to call su beforehand.
Otherwise, you can do (manually, or I suppose scripted):
pc $ adb -d shell
android $ su
android # ps
android # kill <process id from ps output>