The doctor took a sperm sample from him; does he have to do ghusl?

Firstly: 

Extracting
semen by hand and the like comes under the heading of masturbation which is
haraam, but if that is for the purpose of medical tests and treatment there
is nothing wrong with it, as is explained in the answer to question no.
27112. See also question no.
329 for more information on the
evidence that masturbation is haraam. 

Secondly: 

If the semen
is extracted by means of pressing on the prostate or by some other method,
then one of two scenarios must apply. Either it is emitted with feelings of
pleasure, which is what usually happens, in which case ghusl is required,
according to scholarly consensus; or it is emitted without any feelings of
pleasure, which usually happens as the result of sickness, and without
deliberately making it happen. In this case there is a difference of opinion
among the fuqaha’. The majority of Hanafis, Maalikis and Hanbalis are of the
view that it does not mean that ghusl is required, and this is the correct
view. 

This applies
to one who is awake. As for one who is sleeping, if semen is emitted he must
do ghusl in all cases, whether it came out with feelings of pleasure or
not. 

Shaykh Ibn
‘Uthaymeen (may Allaah have mercy on him) said: The apparent meaning of the
hadeeth (“Water is for water”) is that ghusl is required whether it comes
out gushing and with feelings of pleasure or not. This is the view of
al-Shaafa’i (may Allaah have mercy on him), that the emission of semen in
all cases means that ghusl is required, even if it is without desire and by
any means, because of the general meaning of the hadeeth. The majority of
scholars are of the view that the obligation of ghusl is dependent on
whether it comes out gushing with feelings of pleasure. 

Some
scholars referred only to feelings of pleasure and omitting the idea of
gushing, and said: If it is with feelings of pleasure then it will
inevitably be gushing. The mention of gushing is in accordance with the
verse in which Allaah says (interpretation of the meaning): 

“So let
man see from what he is created!

6. He is
created from a water gushing forth”

[al-Taariq 86:5, 6] 

If it is
emitted without feelings of pleasure when one is awake, then ghusl is not
required. This is the correct view. 

If it is
said: What is the answer to the hadeeth “Water is for water”? 

We say: This
applies to the usual case, which is emission with feelings of pleasure,
which leads to relaxation and tiredness. As for that which is not like that,
it does not lead to relaxation and tiredness. End quote from al-Sharh
al-Mumti’. 

See also the
answer to question no. 12317. 

And Allaah
knows best.