I am trying to make a bar-plot where the plot is ordered from the miRNA with the highest value to the miRNA with the lowest. Why does
Your code works fine, except that the barplot is ordered from low to high. When you want to order the bars from high to low, you will have to add a -sign before value:
ggplot(corr.m, aes(x = reorder(miRNA, -value), y = value, fill = variable)) +
geom_bar(stat = "identity")
which gives:

Used data:
corr.m <- structure(list(miRNA = structure(c(5L, 2L, 3L, 6L, 1L, 4L), .Label = c("mmu-miR-139-5p", "mmu-miR-1983", "mmu-miR-301a-3p", "mmu-miR-5097", "mmu-miR-532-3p", "mmu-miR-96-5p"), class = "factor"),
variable = structure(c(1L, 1L, 1L, 1L, 1L, 1L), .Label = "pos", class = "factor"),
value = c(7L, 75L, 70L, 5L, 10L, 47L)),
class = "data.frame", row.names = c("1", "2", "3", "4", "5", "6"))