No
As long as the break or tear is no larger than 1 foot in any dimension, you mend it (...)
You have stated that the tear in your cloak is longer than 1 foot, so you can't use Mending on it. It doesn't matter if the cloak itself fits within a 1 foot cube, since at least one of the tear's dimensions (its length) is larger than 1 foot, even if you fold it.
You might, however, want to try something like sewing it in the middle so that you have two smaller tears, and Mending it then, but only if your DM is prone to allow such shenanigans. Or just ask them directly if you could Mend your cloak, Mending does not usually influence the plot or gameplay in a major way, so he might just waive the constraints on it this time.
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.
Best Answer
Mending doesn't create new bond; it restores a broken one
The answer by Exempt-Medic already covers the basics: Mending repairs a single break in a single object, not multiple breaks in multiple objects. However, I want to answer the part of your question about affixing two objects together by first gluing them, then breaking the joint and fixing it with Mending.
So, let's take the specific example you gave, in which you glue together 2 polished steel parts with wood glue. First of all, I'm not convinced that wood glue will even stick to a smooth polished steel surface at all, but that's a real-world question, not a D&D rules question. So for the sake of argument, let's assume wood glue can weakly affix 2 steel surfaces to each other.
So, you create your combined object: 2 steel pieces glued together by a very weak joint of wood glue between them. Now, you break the 2 steel pieces apart at this weak joint, and then you cast Mending to put them back together again. What do you get? Well, here's what Mending actually does:
In other words, you undo the damage that caused the break or tear, leaving you with the same object you had before it was broken apart: 2 steel pieces glued together by a very weak joint of wood glue. You definitely don't get 2 steel pieces magically welded together, unless that's what you started with.
Mending is a limited "undo button"
Here's another way to think about it: Mending is like an undo button. It can revert an object to a previous state, provided that the object's current state differs from that previous state in a specific way (i.e. the difference must be a single small break or tear). Mending can never put an object in a new state that it hasn't been in before, such as creating a welded steel object from 2 steel pieces affixed with wood glue.
So yes, in a certain sense, Mending really does "know" whether or not the two pieces you're trying to join back together were originally part of the same object, because it is only capable of joining them back together if they really are pieces of the same object. Just like how Hold Person "knows" what is and isn't a humanoid, in the sense that it only works on humanoid targets. In both cases, the spell doesn't really know the difference; it just fails when you cast it on an invalid target.