RAW yes, RAI probably not.

RAW:

Let's analyze Mending's description:

This spell repairs a single break or tear in an object you touch, such as a broken chain link, two halves of a broken key, a torn cloak, or a leaking wineskin. As long as the break or tear is no larger than 1 foot in any dimension, you mend it, leaving no trace of the former damage.

This spell can physically repair a magic item or construct, but the spell can't restore magic to such an object.

• "a single break or tear": the dictionary defines a tear as "a hole in a piece of paper, cloth, or other material, where it has been torn"; being torn is defined as "to pull or be pulled apart, or to pull pieces off". If a giant rips off your arm, that clearly fall into the category of "pulled apart", therefore it would be considered a tear. Technically, if a knight cut off your head instead, that would not be "torn off", but for the sake of argument, let's just assume that any severed body parts count as "torn off" - it wouldn't make any sense if the spell could repair a ragged, ripped-off head, but not a cleanly cut off head (or other body part, for that matter).
• "object you touch": unless you have necrophobia, you'll probably be able to touch your companion (and if not, you can't use Revivify either). And, as mentioned, corpses are considered objects.
• "As long as the break or tear is no larger than 1 foot in any dimension": My reading here is that it doesn't matter how big your head is, as long as the part where it is severed is only 1 foot in any direction. This should be true for most necks or other points of dismemberment unless you got cut in half at the hip (or vertically. Ugh.)
• "you mend it": defined as "to repair something that is broken or damaged" - this is the case here. If a severed head doesn't count as "damaged", I don't know what does.
• "leaving no trace of the former damage": this suggests that all internal organs, arteries etc. are healed, otherwise, there would be "a trace of the former damage".
• "This spell can physically repair a magic item or construct, but the spell can't restore magic to such an object": this only applies to magic items and constructs, but even if it didn't, it wouldn't matter, since your head (probably) isn't attached by magic means.

Therefore, we can conclude, that RAW, Mending can be used to "heal" / repair dismembered corpses. The corpse will still be a corpse, but it now qualifies for spells like Revivify or Raise Dead (none of which could otherwise restore missing body parts).

Note that, due to Mending's 1-minute casting time, you'll have to take measures such as casting Gentle Repose, otherwise, you won't be able to use Revivify, which only works within 1 minute of the target's death.

RAI:

There is a spell dedicated to restoring or reattaching dismembered body parts, Regenerate, which is a 7th-level spell. Granted, it also restores hit points when cast and over time, but still way higher level than an at-will cantrip.

Furthermore, the higher-level resurrection spells like Resurrection and True Resurrection explicitly specify that they restore missing body parts, while Revivify and Raise Dead explicitly specify that they cannot. The intent seems to be that restoring missing body parts is a high-level feature.

In conclusion, using a cantrip and a 3rd-level-spell to partly emulate the effects of the 7th-level spell Resurrection (without restoring all hit points or curing poisons and diseases) does not seem to be the intent. In addition, the language of the Mending spells suggests that it is meant for objects other than corpses, since it makes no mention of those.

Conclusion:

Whether or not you can use this combination therefore depends on your DM. I personally don't think I would allow it - but then again, introducing any limb-loss mechanics into the game is homebrew territory anyways and, if at all, will only happen due to RP reasons in games that I DM, such as a thief choosing to have his hand chopped off instead of going to prison.