The pump is COMPLETELY irrelevant to muscle growth.
The only benefit is purely psychological in that it makes people feel good while working out & makes it easier to establish the mind-muscle connection to ensure your working the targeted muscle.
I should note that you don't need the pump to actually work the muscle, especially if your form & time under tension is appropriate, it simply helps some people in this aspect.
If its really an issue for you then here are a few causes & possible solutions:
The pump can be reduced if your carb intake is too low but more importantly if your in a caloric deficit - if your cuttingat the moment its inevitable your pump will be low.
Fat intake as an isolated macro does nothing for blood flow during resistance training so that's not the issue.
We cant rule out overtraining, although I'm skeptical of this unless its high activity + low calories type of thing.
A diet solution would be to increase your carb intake slightly preworkout - a fast acting carb (think sugars, a few cookies, honey, etc) 20 mins before lifting will do the trick.
A training solution would be a combination of reducing the frequency/volume of your sessions & increasing the time under tension.
For frequency, lift no more than 3-4x week.
For volume, it depends on what your doing now but something like 4-5 exercises/2-3 sets per move/8-15 reps per move.
Time under tension is key for a pump - you want to take 3 secs to contract the muscle, 6 secs on the eccentric portion. This will rapidly increase blood flow & give you the pump your looking for but I warn you that it makes workouts & recovery alot more difficult so its essential to keep frequency/volume low.
Just a few things to consider