Heroic Silverware Golem can be finished off easily by turning his strength into his weakness, the fact he always summons 2 plates. The strategy is letting him fill his board with plates - which he does right away at the beginning of his turns - then keep those plates alive at 1 attack to deny further minions to be played by him and heal ourselves through the whole of the game mainly with Lightwells.
Mulligan for Lightwell and Power Word: Shield. Shieldbearer helps slow down the beginning of the game without killing the plates, while Shadow Word: Death helps getting rid of early knifes that threaten your Lightwells.
By turn 3 he should have 6 plates and something else down. Kill whatever the 7th minion is ASAP and focus on buffing up your Lightwells HP with Power Word: Shield and Divine Spirit and create copies of them with Faceless Manipulator. Don't use Inner Fire because plates might suicide into your Lightwells, we want the plates alive, Inner Fire is for finishing Silverware Golem off only.
Once his board is filled with plates and you have Lightwells up, all you need to do is silence the plates when they get buffed by the only 2 buffing spells Silverware golem has - use Mass Dispel preferably.
From this on you just watch him burn through his deck while you are at full health all the time. Use Mind Blast and Embrace the Shadow to help burn his health and use Inner Fire on your buffed Lightwells ONLY when you can kill him with them.
Update for Un'goro: Removed wild cards and added Binding Heal, Shadow Visions and Holy Fire. Shadow Visions provides excellent value and will help you to get a copy of a spell required to build up your healing machine, silence enemy minions or kill those pesky cutleries.
Wild cards to swap in if you have them:
If this helped to defeat Heroic Silverware Golem please give a +1, cheers.