Is it true that mitosis is how you reproduce asexually while meiosis is how you produce sexually?

Yes, in a way. Bacteria reproduce by mitosis, since they just need to copy themselves and another organism exists. (thus, asexual)

Humans and other animals that reproduce sexually need to go through meiosis to produce haploid cells (aka gametes) so their offspring doesn't end up with double the number of original chromosomes, consequently producing another species in a sense (that's for another question, so I'm not going to go into details).