A node-sass custom importer which turns ~ into absolute paths to the nearest parent node_modules directory.

npm install node-sass-tilde-importer --save-dev

var sass = require('node-sass');
var tildeImporter = require('node-sass-tilde-importer');

var result = sass.renderSync({
  data: scss_content,
  importer: tildeImporter
});

node-sass cli example:

node-sass style.scss --importer=node_modules/node-sass-tilde-importer

Please refer to the node-sass readme for full instruction on how to use custom importers.