Beshrew that heart that makes my heart to groanFor that deep wound it gives my friend and me. (1-2)
When our speaker accuses his mistress of giving him and his buddy a "deep wound," he means a couple of different things. On the one hand, he means that she's hurt their feelings by being romantically involved with both of them at once. On the other hand, he's also punning on the word "wound" in order to make a crude joke. "Wound" is slang for "vagina," so he's saying that, when she gives him her "deep wound," it make makes him "groan" in ecstasy. Presumably, this is why our speaker is so tortured. He knows his mistress is a no good cheater, but he really likes hooking up with her and doesn't feel like he can stop. This is probably true for his friend, too.
Is't not enough to torture me alone, But slave to slavery my sweet'st friend must be? (3-4)
Gee. Our speaker sure is dramatic when he accuses his mistress of torturing him and then running out and turning his BFF into her "slave." Now, the word "slave" can mean a few different things, but given the "deep wound" joke in the previous lines, it seems like our speaker is accusing his mistress of forcing his friend to perform a lot of physical or labor intensive acts. He may also be suggesting that his buddy is addicted (a "slave to slavery") to having sex with her.
And my next self thou harder hath engrossed. (6)
If you're thinking this line sounds a little dirty, you're definitely onto something. After our speaker accuses his mistress of having "taken" possession of him (5), he accuses her of having "engrossed" his buddy (a.k.a. his "next self") even "harder" (6). In other words, she's also taken our speaker's friend away from him and acts like she totally owns the dude. Of course, there's an erection joke happening here, too—"engross" can also mean to make something bigger or fatter so, it sounds like the mistress gives the friend a bigger manhood than she gives the speaker.