Deleting data by location using another shapefile

I suppose that you have two layers with overlapping objects.

Processing → Extract by location.

Extract features from the main layer by comparing them with features from second layer. The predicate is disjoint. After launch, you'll get the layer without points from the second layer.

If those overlapping features (points from the divided part) share the same location with features (points from the main layer) I will simply use the "Difference" from the Vector > Geoprocessing Tools > Difference.

This algorithm extracts features from the Input layer that fall outside, or partially overlap, features in the Overlay layer. Input layer features that partially overlap feature(s) in the Overlay layer are split along those features' boundary and only the portions outside the Overlay layer features are retained.

Attributes are not modified, although properties such as area or length of the features will be modified by the difference operation. If such properties are stored as attributes, those attributes will have to be manually updated.