One should wash all around the cut and perform tayamum for the wound itself (However, if one has chicken pox, or a severe acne problem then he should wash between them if there is no harm in doing so, otherwise, he should not).

If it is for major hadath, one can perform tayamum before ghusl or afterwards because the whole body is considered one part in ghusl and there is no prescribed sequence.

If it is for minor hadath then one should do it in its proper sequence and not move on from one part to the other until he has washed and/or performed tayamum for it.

It does not matter whether one washes the part first and then performs tayamum or vice versa.

If the injury is in two different parts then two tayamums are necessary and if it is in three parts then three tayamums are necessary.

However, both arms are regarded as one body part as are both legs.

Hence, if there is an injury in both of them then only one tayamum is necessary.

However, it is recommended to regard them as two parts and perform tayamum for each one of them after washing the sound area of each.

If the injury is not in one of the body parts of tayamum (face and arms), it is not necessary to wipe it with water or earth even if it does not cause any harm.

However, if the injury is in one of the parts of tayamum then the injury must be wiped with earth if there is no harm in that.

In the case it might be harmful, like someone with chicken pox on his face, then one can follow the rules of lacking the two purifiers with respect to his face (Similarly, if one has an eczema, or the like, on his face or arms or both then he can apply the rule of lacking the two purifiers to those parts (face or arms) which may be harmed by earth and he is excused of the obligation), and he must wipe his arms following the rule that says difficulty breeds facilitation. He should re-perform these prayers when able to use water or earth. (pa: 74)

In all cases of tayamum for an injured part on which there is no bandage, it is not obligatory to repeat prayers because this is a common affliction except in the above excluded case.

If there is profuse blood in the wound that cannot be excused, and it is feared that washing it will cause harm, then one should repeat the prayer because he prayed while having najasa on his body.