A remix starts from one song
A mashup combines parts of two or more existing recordings. A remix keeps one song at its centre and replaces most of what surrounds it: new drums, new bass and chords, often a new tempo and genre. The usual core you keep is the vocal, sometimes with one signature hook from the original.
That means most of the work is production rather than matching. You are writing a new track that the original vocal can live in.
Get the parts
Official stems from a remix contest or the artist are the best source, because each part arrives clean and at the original tempo. If all you have is the finished song, separate the vocal with a stem-separation tool and accept some artifacts. Note the tempo and key of the vocal before anything else; every later decision depends on them.
Check what you are allowed to do with the result. Contest stems usually come with terms for where you can post your remix, and an unofficial remix of a commercial release needs permission before you distribute it.
Choose a new tempo and feel
Decide what the remix is for: a club edit, a slower acoustic take, a drum and bass version. Then choose a tempo that the vocal can reach cleanly. Small stretches (a few percent) are transparent. For a big genre jump, count the vocal at half or double time: a 87 BPM vocal sits naturally on a 174 BPM drum and bass beat without being stretched at all.
If you change the key, keep the shift to a semitone or two, or the voice starts to sound unnatural. It is usually better to write the new chords in the vocal’s original key.
Build the new track under the vocal
Start with the chorus. Loop the vocal’s chorus and write drums, then a bassline, then chords that fit its melody; the original chords are a safe guide, but re-harmonising with different chords in the same key is where many remixes find their character.
Keep the arrangement simpler than the original. A remix vocal is competing with new sounds, so leave space in its frequency range and mute parts when the vocal is busy. Tempo-synced delays and reverbs help the vocal sit in the new track; the BPM to ms calculator gives the times.
Arrange for the new context
Remixes for DJs usually get longer intros and outros with a steady beat, so they can be mixed in and out; 16 or 32 bars of drums before the vocal is common. Listening versions can be closer to the original structure.
Bring the original hook in where it has the most effect, such as after a breakdown, rather than repeating it constantly. Then check the mix against the original song at the same loudness: the vocal should be just as clear in your version.
Credit it properly
Title remixes in the standard way, with the original artist and title and your name in brackets, such as “Song Title (Your Name Remix)”. Credit the songwriters and original artist wherever you post it.