Yes, the effects of Minor Healing are cumulative
The description of the spell (HARP rulebook, p113) states the following:
These options each constitute the definition of a Light
injury as described in Chapter 9, Healing Injury & Death.
This might lead you to conclude that the Minor Healing spell only works on Light injuries, while the Major Healing spell (HARP rulebook, p119) is required for anything more serious than that.
However, the aforementioned Chapter 9 (page 80) says:
Damage that a character receives is
classified into three severities, based upon the total
amount of damage he has received from all wounds. That
means that any and all damage from Hits and Criticals are
added together to determine the severity of damage that
the character has taken.
So the effects of damage on the character are cumulative: multiple Light injuries might add up to a Medium or Severe injury. Therefore it makes sense that the effects of magical healing are also cumulative: one Minor Healing spell might reduce the severity from Medium to Light, then a second spell would heal the remaining damage.
For example, a character might receive three criticals that each impose a -20 maneuver penalty. Together, these add up to a Severe injury. However, if the character casts Minor Healing on themselves after receiving the second wound, they can reduce the penalty from -40 (Medium) to -20 (Light). The third injury then increases the severity to Medium again. Why should it matter whether the character casts the spell after receiving the third wound, or before?
Another example of how this spell can be cast multiple times for cumulative effect is the 3 Power Point version of the spell. It can either reduce a maneuver penalty, reduce bleeding or heal concussion hits. The spell can be cast once to treat bleeding and a second time to restore concussion points. Alternatively, the 5 PP version of the spell can treat both problems with a single casting.
The relationship between the Minor Healing spell and Major Healing is that the latter spell has a greater effect per individual casting. A Cleric with Major Healing can restore 50% of a character's concussion hits with a single, 4PP spell. Two successive castings of Minor Healing would have the same effect.