According to F=ma, can the increase of acceleration lower the mass of a rigid body?

F=ma is a relational or cause-effect physical characteristic observation.

It is not a material property formula.

It meaning is:

Force will cause a mass to accelerate
OR
An accelerating mass will generate Force

Since the rigid body mass is determined/fixed by its physical property, it will not change just by acceleration, increase of acceleration will only increase the force it generate or excreted upon.

The answer is No in "normal" acceleration.

F=ma, can the increase of acceleration lower the mass of a rigid body?
No, that is not the case !
[ Note: the mass of a rigid body is always CONSTANT (物質不滅論) ]

The application of this formula should be, as in the following eg. :-
With the same force F,
a steel ball of mass M running on a frictionless table can accererlate at x km/h ;
a steel ball of a smaller mass m running on this table would have an accererlation > x km/h