There is a function to get the k-smallest value from a list in the STATISTICS group of functions. Its name is simply SMALL.
Let the range be $A$11:$A$100 and let’s assume you want to exclude the lowest three values from the sum over that range.
=SUM($A$11:$A$110)-SMALL($A$11:$A$110;1)-SMALL($A$11:$A$110;2)-SMALL($A$11:$A$110;3)
or
=SUM($A$11:$A$110)-SUMPRODUCT(SMALL($A$11:$A$110;ROW($A$1:$A$3))
will do so. Using SUMPRODUCT for the second part will evaluate its parameter as an array expression. The range $A1:$A3 as parameter of ROW will therefore generate the sequence {1, 2, 3} over which the second parameter of SMALL will then iterate. SUMPRODUCT will add the three results.
To be more flexible you might want to parametrise some constituents of the expression. You may ask for further advice if interested.
(I attach this example.)