You can do this on each series / column using str.replace :
In [11]: s = pd.Series(['potatoes are "great"', 'they are'])
In [12]: s
Out[12]:
0 potatoes are "great"
1 they are
dtype: object
In [13]: s.str.replace('"', '')
Out[13]:
0 potatoes are great
1 they are
dtype: object
I would be wary of this throughout the DataFrame, because it also changed non-strings columns to rows, however you could iterate over each column:
for i, col in enumerate(df.columns):
df.iloc[:, i] = df.iloc[:, i].str.replace('"', '')
, , applymap:
df.applymap(lambda x: x.replace('"', '')