Ubuntu Mate only provides instruction how to use Linux to download and install the image to a microSD card, so here is how you can do it for Mac OS X.
Download Ubuntu Mate from https://ubuntu-mate.org/raspberry-pi/
You will need xz tools to unpack the archive, if you don’t have it installed you can use homebrew
brew install xz
Go to your directory where you have downloaded Ubuntu Mate and unpack the image
xz -d ubuntu-mate-15.10.3-desktop-armhf-raspberry-pi-2.img.xz
Insert your microSD card and locate the drive, it will be named like /dev/disk3 (or whatever the number is representing your microSD card)
You Will need to unmount the disk so we can use dd to write the image.
diskutil unmountDisk /dev/disk[your-id]
When unpacked you can install the image as usual by using dd. Try using rdisk instead if you can, it’s much faster. Just change the name from /dev/disk[your-id] to /dev/rdisk[your-id]
sudo dd if=ubuntu-mate-15.10.3-desktop-armhf-raspberry-pi-2.img of=/dev/rdisk[your-id] bs=1
It will take some time, specially if you used dd. When it’s done, just remove the card and use it to boot your Raspberry Pi 2/3.