Cropping a large geotiff in QGIS

The problem is in your input extent, you defining extent from other CRS so the Clipper trying clip the:

-61.0812601912316993,13.7067470580471564 : 60.8717473436720837,14.1115003832598784

to

507118.619912,1549423.97735 : 511757.851837,1546542.77015

Which makes raster much bigger ("thousands of TB") than base raster 150MB

You have to reproject your input raster to CRS you are using, or in clipper extent use EPSG:4326 (+proj=longlat +datum=WGS84 +no_defs) coordinates.

Layer Spatial Reference System
+proj=longlat +datum=WGS84 +no_defs
Layer Extent (layer original source projection)
-61.0812601912316993,13.7067470580471564 : -60.8717473436720837,14.1115003832598784

Your raster is in longitude-latitude coordinates, but you are trying to clip it using UTM coordinates, so you're actually creating a much larger raster, rather than cropping it into something smaller. You have two choices: use lat-long coordinates in the clipper, or reproject the raster to the utm coordinate system of your choice using the Warp(Reproject) tool under the raster menu.