Can I say?
1 He / She is a doctor, the doctor is mine.
2 They are doctors, the doctors are mine.
3 It is a pen, the pen is mine.

4 This / That is a book. The book is mine.
5 These / Those are books. The books are mine.

6 That doctor is mine.
7 These / Those doctors are mine.

And if I am a lord, so can I say:
8 He / She is a slave, the slave is mine.
9 They are slaves, the slaves are mine.
10 That slave is mine.
11 These / Those slaves are mine.

Question

Can I say?
1 He / She is a doctor, the doctor is mine.
2 They are doctors, the doctors are mine.
3 It is a pen, the pen is mine.

4 This / That is a book. The book is mine.
5 These / Those are books. The books are mine.

6 That doctor is mine.
7 These / Those doctors are mine.

And if I am a lord, so can I say:
8 He / She is a slave, the slave is mine.
9 They are slaves, the slaves are mine.
10 That slave is mine.
11 These / Those slaves are mine.

Answer

3,4,5 are correct.
6 is incorrect. Singular 'doctor' does not go with 'are'.
1,2,7 are probably grammatically correct, but we don't normally use 'mine' with people. You could say 'that is my doctor', but not 'that doctor is mine'. The first means 'that is  the doctor that I visit'. The second means 'that is the doctor that I own'. 
The only exceptions to that are when you are referring to someone very close, like your girlfriend/boyfriend/husband/wife, or possibly if you control them in some way.

Answer

1, 2, 3, 8, and 9)
These are comma splices. They are each two independent clauses connected by a comma. You need to replace the comma with a coordinating conjunction or semicolon. You can also say, "It is a pen, my pen", where "my pen" is an appositive. And you can do the same for the other 2.

6, 7, 10, and 11 are all correct.

Answer

This practice has 8 doctors. (pointing) He is a doctor. He is mine. (my doctor)

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