Please read through the ComplexHeatmap manual, especially the section on row and column orders: https://jokergoo.github.io/ComplexHeatmap-reference/book/a-single-heatmap.html#get-orders-and-dendrograms-from-heatmap
You can use row_order and column_order following a draw() (which you can nest between a pdf(null) and dev.off() to disable drawing it on any ...
I've used some dummy data for simplicity. It's fairly easy to do this with ggplot, but you have to format your matrix-like data for ggplot input.
# make data
ngenes <- 20
nsamps <- 10
my_dat <- matrix(rnorm(ngenes*nsamps), ncol = nsamps, nrow = ngenes)
colnames(my_dat) <- paste("samp", seq_len(nsamps))
rownames(my_dat) <- ...
What is fed into ComplexHeatmap is what it outputs! So if one of your genes has a Missense_Mutation as well as a Frame_Shift_Del and you would like to plot its value, of course you will have a category and color that is different than those of Missense_Mutation or Frame_Shift_Del, that is only natural.
What you can do is to create additional variables like ...