Seems a funny way of putting it, but its meaning is clear from "siendo accesorias el resto de la lesiones".

Some examples:

"the scientific evidence seems to point towards the obstruction of the blood vessels as the main mechanism of death."

"The ultimate mechanism of death is almost always a lethal arrhythmia"

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Note added at 2 hrs (2019-09-09 19:47:50 GMT)
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Depending on how literal / formal a translation is required, I also agree with Phil's answer.

As prescribed by regulatory authorities.

The underlying cause of death is the disease or injury that started the sequence of events leading directly to death or the circumstances of the accident or violence that produced the fatal injury.
https://www.cdc.gov/nchs/data/misc/hb_me.pdf
The MCCD is set out in two parts, in accordance with World Health Organisation (WHO) recommendations in the International Statistical Classification of Diseases and Related Health Problems (ICD). You are asked to start with the immediate, direct cause of death on line Ia, then to go back through the sequence of events or conditions that led to death on subsequent lines, until you reach the one that started the fatal sequence. If the certificate has been completed properly, the condition on the lowest completed line of part I will have caused all of the conditions on the lines above it. This initiating condition, on the lowest line of part I will usually be selected as the underlying cause of death, following the ICD coding rules. WHO defines the underlying cause of death as “a) the disease or injury which initiated the train of morbid events leading directly to death, or b) the circumstances of the accident or violence which produced the fatal injury”...You should also enter any other diseases, injuries, conditions, or events that contributed to the death, but were not part of the direct sequence, in part two of the certificate.
https://www.gro.gov.uk/Images/medcert_July_2010.pdf
Towards the end of an autopsy report is the pathologist's opinion as to the cause of death, which should be presented in the standard manner prescribed by the Office for National Statistics (ONS)28. The main pathology, or the underlying cause of death, is the bottom line used in part one of the statement; significant contributing diseases are placed in part 2 of the statement.
https://www.ncepod.org.uk/2006Report/results_of_study_13.htm...

The original "íntimo", meaning deeper, innermost, refers to the principal or fundamental cause of death. Legally, it could be called the immediate cause of death, as this is what the original conveys -although this is not fully correct; the immediate cause of death would be the haemorrhage and/or fatal lacerations due to the cranial fracture.

Anyhow, rather literally, I would refer in this particular case to the immediate mechanism of death [immediate, fundamental, principal mechanism of death]


Some legal notes related to our case;

Immediate cause of death: The final disease or injury causing the death. Intermediate cause of death: A disease or condition that preceded and caused the immediate cause of death. Underlying cause of death: A disease or condition present before, and leading to, the intermediate or immediate cause of death.
https://www.mdedge.com/familymedicine/article/60314/cause-de...

Immediate mechanism of death:
Septic shock (days)
Enterococcus bacteremia (days)
Acute Respiratory Distress Syndrome (days)
Disseminated intravascular coagulation (hours)
Underlying disease:
Hepatitis C cirrhosis (years)
https://www.google.es/url?sa=t&source=web&rct=j&url=https://...

Suppose a child falls off a bicycle, suffers a cranial fracture, and dies from a cerebral hemorrhage. On the death certificate the immediate cause of death is listed as a cerebral hemorrhage, due to or as a consequence of a cranial fracture (intermediate cause), which was due to or as a consequence of a fall off a bicycle (underlying cause).
https://www.encyclopedia.com/education/encyclopedias-almanac...