Ruling on offering as a sacrifice a sheep whose tail or buttock has been cut off; what is the ruling if no intact animal can be found?

Firstly: 

It is essential to differentiate between an animal whose tail
has been cut off and an animal whose buttock has been cut off, when it comes
to offering the sacrifice. If the tail has been cut off, that does not
affect the validity of the sacrifice, unlike one who buttock has been cut
off, according to the most correct scholarly view. 

Ibn Qudaamah al-Maqdisi said: 

It is acceptable to offer an animal that has no tail, whether
it was born that way or had its tail cut off, because this is a defect that
does not affect the meat and does not undermine the purpose, and there is no
report to indicate that it is not allowed.

End quote from al-Mughni (13/37 2) 

And he said: 

It is not acceptable to offer any animal that has had part of
its body cut off, such as a buttock.

End quote from al-Mughni (13/371) 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:

An animal that has no tail, either because it was born that
way or had its tail cut off, is acceptable… As for that which has had its
buttock cut off, it is not acceptable, because the buttock is a valuable
part of the body that people would want. 

Based on that, if a sheep has had its buttock cut off, it is
not acceptable, but if a goat has had its tail cut off, it is acceptable.

End quote from ash-Sharh al-Mumti‘ (7/435) 

He also said:

As for that which has had its buttock cut off, the scholars
said: It is not acceptable, because the tail is beneficial and is something
that people would want, unlike the tail on goats, cattle and camels, which
is not something that people would want, and therefore may be cut off and
disposed of. The same applies to the tail of Australian sheep. It is not
like the buttock; rather it is like the tail of cattle, and is not something
that anyone would need. So it is acceptable to offer an Australian sheep as
a sacrifice (udhiyah), because the cut-off tail does not have any value. 

End quote from Jalasaat al-Hajj (p. 108)

We have previously quoted the fatwa of the Standing Committee
about it not being permissible to offer as a sacrifice an animal that has
had its buttock cut off, in the answer to question no.
37039

Secondly: 

What you must do is try to look for a sacrificial animal that
has not had its buttock cut off, and it is not acceptable for you to offer
as a sacrifice a sheep that has had its buttock cut off so long as it is
possible to obtain a sheep that is free of all faults. 

If you are not able to obtain an intact sheep, then what is
prescribed in this case is to move to another type of an‘aam animal
[livestock animals, which includes camels, cattle, sheep and goats] that is
acceptable as a sacrifice. So you should forget about these defective sheep,
and sacrifice goats, if you can find goats that are free of defects, or
sacrifice cattle (or buffaloes), or camels. Seven of you can share in
sacrificing a cow or a camel, or anyone who wishes may sacrifice a cow or a
camel on his own. It is permissible for him to do that, and if less than
seven share in that, that is permissible, but no more than seven should
share in sacrificing a single cow or camel. 

But if it is not possible to obtain a sheep that has not had
its buttock cut off, because all the available sheep in the country are like
that, and you cannot sacrifice other an‘aam animals instead, in the manner
explained above, then what appears to be the case in this situation is that
it is acceptable to offer such a sheep as a sacrifice, especially as the
owners of the sheep do that to them in their best interests, and they do not
regard that as a defect that detracts from their value, because saying that
it is not allowed in this case would result in cancelling out one of the
rituals and symbols of Islam. 

The interest of openly practising the ritual of sacrifice (udhiyah)
outweighs the negative consequences of offering a specific animal as a
sacrifice. The well-established principle among the scholars is that that
which is within one’s means to do is not waived because of that which is
beyond his means. 

In other words, if it is not possible to do something in the
required manner, but it is possible to do part of it, it is not waived;
rather we should do whatever we are able to do of it. 

This principle is based on the words of the Prophet
(blessings and peace of Allah be upon him): “If I command you to do
something, then do as much of it as you can.” Narrated by al-Bukhaari (7288)
and Muslim (1337). See also: al-Ashbaah wa’n-Nazaa’ir by as-Suyooti
(p. 159) 

Al-‘Izz ibn ‘Abd as-Salaam said: Whoever is required to do an
act of obedience, but he is able to do part of it and not able to do part of
it, then he should do whatever he is able to do, and whatever he is unable
to do will be waived in his case.

End quote from Qawaa‘id al-Ahkaam (2/7) 

And Allah knows best.