DFT of sum of sinusoids with random zeroed samples
The math is well known; it is the convolution theorem for the DFT.

In this specific case:

$$DFT\left\{f[n]\cdot z[n]\right\} = DFT\left\{f[n]\right\} * DFT\left\{z[n]\right\}$$

Where:

$f[n]$ denotes your original sequence of 128 samples

$z[n]$ denotes a sequence of 128 samples, each randomly selected from $\{0,1\}$

'$*$' denotes cyclic convolution, since we're talking about the DFT.

The results of this convolution are visible in your second plot, particularly at very positive and very negative frequency bins.