"Accumulating Genetic Accidents" and selection

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Many times, for many years I have been saying the mechanism proposed by the theory of evolution is nothing more than an accumulation of genetic accidents.

My reasoning is as follows:

In the evolutionary scenario all mutations are genetic accidents. And those accidents have to accumulate- they do so by various selection processes as well as sheer dumb luck.

But if they do not accumulate then evolution wouldn't go very far.

Richard Dawkins calls it "cumulative selection"-

What is the point?

Jeffrey Shallit doesn't seem to understand that mutations accumulate.

Also the best he can do is provide evidence for Common Descent- evidence for Common Descent is not evidence for accumulating genetic accidents.

The point of my query was to test the MECHANISM.

However it is obvious that testing the proposed mechanism is just a pipe-dream.