To accomplish your goals, including booting, you're wanting to do two things. One is to copy the first two partitions. The other thing you're seeking to do is to copy the boot process. With a traditional MBR format, which you might be using, the boot process is contained in first 512 bytes of a disk, which is called the MBR. This is not part of either of those partitions. (The other part of the boot process is contained in the partitions that get copied over.)
If you're using GPT, then the same concepts apply, although the boot sequence will involve more than just the first 512 bytes of the disk. Some tools work better with GPT than others.
You might be easiest to just do a complete image copy. Of course, the copy will fail since you'll run out of space, but that could simply result in a corrupt partial copy of the third partition, which you could then delete.
Note that instead of trying to copy the existing boot sequence, you might find it easier to just re-create it. Start by just focusing on getting the partitions copied, and making sure that they were correctly written to disk. Then, re-enable booting (by re-enabling the boot code... on MBR disks this was often described as re-installing the MBR). With Windows 7, BCDEdit may be useful for this.