This is normal. First you need to evaluate this guide: http://www.elite-strategies.com/flavors-types-google-penalties/ and see what kind of penalty you have. Then you need to get all data from Analytics, Search Console both Links and Analytics there.
And here is huge analysis...
- You need to check timeframe of your sudden drop. Are there some turbulence in SERP? New algo released? Anything weird in your own castle (server, CMS, hosting provider, etc)? If there is something - fix it. Also read about algos/turbulences in industry news sites.
- Check for messages in SearchConsole about "Manual Actions" and fix them if it's any.
- Check for sudden change of your links and create linking profile. If there are new and weird links from spammy sources - disavow them ASAP. If there is overoptimization for keywords - change anchor or disavow. This can be something Penguin algo related.
- Check for sudden change of your site - thin content, aggregated content, duplicate, irrevelant, etc. Check also user signals - low CTR, high bounce rate, low time on site and low % of returning users. Also check bad UI - design, navigation, mobile redirects, site speed, ads. Check for low trustworthiness - in Google Raters Handbook that was recently released. This can be - providing contact information, ToS, PP, etc. And last - overoptimization. This can be something to Panda algo related.
- Check for other algorithms - like TopHeavy aka Page Layout Algorithms that may affect your site.
So after you know what can be your drop related then check and recheck. Isn't first nor last time when you can think about Panda but in reality was Penguin or vice versa. This can save you few months. After you're 100% sure what was then try to make changes to escape from algo penalty.
Same happens to me almost year and half. We're running brand new site and faced sandbox algo. But we make few links more than we should and from low quality sites. So site was shown in SERP for month in first or second page and then suddenly drop to 10 page. Our organic traffic was fell to 1/10 of before almost overnight. But we make new traffic sources - social media and referral traffic so we could live without organic. We change links, make diversify linking profile changing links, anchors or even both. We also delete some links. But nothing happen in SERP position. Then i use disavow tool and 2 weeks ago there was algo refresh (Penguin). Almost overnight search traffic jump more than 10x and recovering previous positions and getting new and ever better positions. Today - this site make traffic as 10x than after recovering.
The problem is that you need to make changes in site against penalty. And wait for algo refresh. You also need huge patience because some drop can happen anytime, but for recovering you need algo refreshes. And refreshes take months or even years.