SoundCloud has working online downloaders from Google. MixCloud however does not.
If you dont want to installer a software called JDownloader, use this method for obtaining URL links for the music..

I'll use pics.

Step 1 - "When you think"

Step 2 - "Finding your mixcloud link for any artist (I havent heard this mix so Ill use it as an example)"

Step 3 - "Realizing the mix does not have a download button can be gear-grinding!!!"

Step 4 - "With Google Chrome, Right-Click a blank spot of the website, then click Inspect Element; next you should click NETWORK"

Step 5 - "Look for extensions of audio formatting (IE: MP3, M4A, ACC, ect.) ; as well as the increasing timeline bar.

Step 6 - "Open the link in a new tab, and as it loads you want to go to the main mixcloud page from step 3, then press BACK on your browser to stop the stream. DO NOT PAUSE!!!"

Step 7 - "Once the page loads, simply RIGHT CLICK and press SAVE AS!!"

Step 8 - "Double check ? I like to do it, mainly so I can remember where the file is being saved."

Step 9 - "Profit?!?"

Brought to you by me for you !