Anglo-French mortgage joined mort, dead, with gage, a pledge or security. Middle English morgage lies on the way to the familiar English form.
The question scores the component meanings, not a particular explanation of why the pledge was called dead.
Sources
- Merriam-Webster: mortgage
The etymology identifies the compound and its Anglo-French and Middle English forms.
- Merriam-Webster: gage
Noun (2) and its Word History establish the pledge sense.
- Online Etymology Dictionary: engage
Also built on *gage*: engage, from Old French engagier, from en gage "under pledge" (gage "pledge")