Devil's Advocate answer: No. (Or, only with written language also.)
A lot of answers here are saying yes, and for good reasons. However, to play Devil's Advocate, I believe there's also a compelling case for non-vocal human beings never achieving the same level of advancement.
Sign languages can be equally complex as spoken languages, and the barriers of use in certain contexts are likely not sufficiently high as to make it practically inferior to spoken language. However, spoken language was not by itself what catapulted human beings to the top of the evolutionary ladder. Written language may have been more important.
You could definitely get to the Agricultural Revolution without written language, but I'm not convinced you could get much further than that. You mention Homo mutus uses "sign languages and written languages", and I think it's worth focusing on this second component. Sign language itself is difficult to write down (though there are ways). You could perhaps end up with an ideographic language representing ideas with characters, but language (even written language) is cognitively understood through phonological encoding (or in Deaf people, through an analogous process, which is why finger spelling is important) and thus must fundamentally be structured in a phonological hierarchy.
Keep in mind that what makes human beings advanced is our cooperation. We use stories and collective fictions to surpass the Dunbar Number (the 150 people in a tribe that you can know simply through everyday interactions). We're capable of cooperating with and trusting other human beings in neighboring villages, simply because they share the same beliefs with us and can communicate productively. This is very important. Equally important as shared belief systems is a use of writing far more mundane, and that's record keeping. It's easy to overlook the effect that record keeping has had on civilization, but no sufficiently large and complex political body could exist without the capacity to keep and preserve detailed records. Record keeping, resource tabulation, mathematics, and so forth, are of the utmost importance. An economic system cannot exist without a written language capable of keeping records. Yes, a barter system works to a certain degree, but is impractical when scaling upwards. Small groups can survive with barter alone. For entire civilizations, it is generally beyond impractical. (Barley coin--despite not being a coin--was decently successful in Babylon, and other cultures have used rice and perishable goods as currency, but even this requires systems of measurement and records of transactions and monetary equivalencies.)
In summary, it isn't spoken/signed communication that's important for advanced civilizations (which is not to say it's trivial), it's written communication and record keeping.