In the case of the ISS various public lists of procedures and equipment do not include instructions or equipment required for blood transfusion. The 2016 list does include equipment to provide saline and procedures and equipment to overcome the absence of gravity appear to have existed since 1993.
It is possible the relevant instructions and equipment are not included in publics lists for various reasons but it is more likely that assessment of the likely injuries on the ISS and the costs involved in supplying multiple blood types of ~30 day shelf life and only when carefully temperature controlled.
Cargo to ISS is infrequent, costing thousands of dollars per kg and not normally refrigerated, so fresh blood would involve more frequent launches and extensive customization of the craft noting power and heat dissipation needed (just packing in dry ice will not fly, literally). There would also need to be safe disposal of non trivial quantities of stale blood every month, where the ISS has occasionally had issues with downmass.
The second element is the actual use for transfusion following injury. For most of the relevant period the ISS had a crew of three, so the assumed action on injury in the linked documents appears to be to stabilise the patient as much as possible and return with hours. While it is possible to die from blood lose in this time frame, the question would be which injuries the surviving two crew could do something useful about with the skills and equipment to hand in the additional time.
It does appear at some point between 2000 and 2016 the on orbit inventory grew to include saline IV solution and equipment to access the bone marrow of the leg to supply it. Saline has a near unlimited shelf life, does not need type match and while not as effective will still sustain circulation in the short term.
Possibly also relevant here is likely injuries - in 0G falling or being fallen on is unlikely, and fire and explosion hazards are rigorously minimised, making the possible events that badly maim a crew member but does not also expose them to space rather limited.
I suspect that if monthly launches of refrigerated cargo was being done most ISS crew would prefer fresh vegetables to blood.
In terms of future space exploration, once your crew size goes past six it becomes rather more likely you will have compatible blood types and the specialized skills to allow collection of donor blood in situ, though hopefully the possibility of injury will remain low through careful engineering.