I think you can use Index.difference:
df[df.columns.difference(dgh_columns)]
Sample:
df = pd.DataFrame({'A':[1,2,3],
'B':[4,5,6],
'C':[7,8,9],
'D':[1,3,5],
'E':[7,8,9],
'F':[1,3,5],
'G':[5,3,6],
'H':[7,4,3]})
print (df)
A B C D E F G H
0 1 4 7 1 7 1 5 7
1 2 5 8 3 8 3 3 4
2 3 6 9 5 9 5 6 3
dgh_columns = pd.Index(['D', 'G', 'H'])
print (df[df.columns.difference(dgh_columns)])
A B C E F
0 1 4 7 7 1
1 2 5 8 8 3
2 3 6 9 9 5
Numpy solution with numpy.setxor1d or numpy.setdiff1d:
dgh_columns = pd.Index(['D', 'G', 'H'])
print (df[np.setxor1d(df.columns, dgh_columns)])
A B C E F
0 1 4 7 7 1
1 2 5 8 8 3
2 3 6 9 9 5
dgh_columns = pd.Index(['D', 'G', 'H'])
print (df[np.setdiff1d(df.columns, dgh_columns)])
A B C E F
0 1 4 7 7 1
1 2 5 8 8 3
2 3 6 9 9 5