It's sad to have to sell off Mother's old furniture.
Literal
Mother [possessive-の] old furniture [object-を] sell-off-[must-なければならない] [nominalizer-の] [topic-は] sad
売り払う = compound verb: sell + sweep-away = to sell off completely. ~なければならないのは悲しい — the entire obligation clause is nominalized (の) and made the topic (は), with 悲しい as the comment. のは...だ structure for making a judgment.